68:@0.058783:0.510692:0.077690:0.510692:0.077690:0.494068:0.058783:0.494068:0.000000:0.000000
Tema:@0.047190:0.135475:0.083321:0.135475:0.083321:0.113749:0.047190:0.113749:0.000000:0.000000:0.000000:0.000000
1. :@0.115209:0.781690:0.133950:0.781690:0.133950:0.764555:0.115209:0.764555:0.000000:0.000000:0.000000
El segundo término de una progresión geométrica es 4 y el octavo término es 256.:@0.148452:0.781690:0.753209:0.781690:0.753209:0.765302:0.148452:0.765302:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.115209:0.805409:0.118931:0.805409:0.118931:0.788274:0.115209:0.788274:0.000000
Calcula:@0.148452:0.805409:0.203883:0.805409:0.203883:0.788785:0.148452:0.788785:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.203883:0.805409:0.207605:0.805409:0.207605:0.788274:0.203883:0.788274:0.000000
lo que se indica en cada literal.:@0.207605:0.805409:0.431022:0.805409:0.431022:0.789020:0.207605:0.789020:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Taller:@0.175844:0.740452:0.236739:0.740452:0.236739:0.706505:0.175844:0.706505:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
I.M.5.4.1. Identifica las sucesiones según sus características y halla los parámetros desconocidos; aplica progresiones en aplicaciones :@0.256865:0.717918:0.877758:0.717918:0.877758:0.707488:0.256865:0.707488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cotidianas y analiza el sistema financiero local, apreciando la importancia de estos conocimientos para la toma de decisiones asertivas. :@0.256865:0.728479:0.877740:0.728479:0.877740:0.718050:0.256865:0.718050:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(J.2.):@0.256865:0.739040:0.277000:0.739040:0.277000:0.728611:0.256865:0.728611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Actividad resuelta:@0.115281:0.500832:0.272404:0.500832:0.272404:0.482395:0.115281:0.482395:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El término   de una progresión geométrica es 2 y el cuarto término es 16. :@0.115281:0.520677:0.665802:0.520677:0.665802:0.504288:0.115281:0.504288:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.195827:0.520677:0.205096:0.520677:0.205096:0.504316:0.195827:0.504316:0.000000
Encontremos:@0.666465:0.520677:0.768130:0.520677:0.768130:0.504053:0.666465:0.504053:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la razón ( ) y la :@0.768130:0.520677:0.884132:0.520677:0.884132:0.504288:0.768130:0.504288:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r:@0.840145:0.520677:0.845434:0.520677:0.845434:0.504316:0.840145:0.504316:0.000000
suma de los cuatro primeros términos.:@0.115281:0.537274:0.396334:0.537274:0.396334:0.520885:0.115281:0.520885:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.115281:0.561809:0.134004:0.561809:0.134004:0.544908:0.115281:0.544908:0.000000:0.000000:0.000000
Sabemos :@0.148525:0.561809:0.222954:0.561809:0.222954:0.545185:0.148525:0.545185:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que   = 2 y que   = 16, de acuerso con:   =   ·     , entonces :@0.221885:0.561809:0.667421:0.561816:0.667421:0.545427:0.221885:0.545420:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.253526:0.561809:0.262795:0.561809:0.262795:0.545447:0.253526:0.545447:0.000000
U:@0.334239:0.561809:0.345295:0.561809:0.345295:0.545447:0.334239:0.545447:0.000000
4:@0.345306:0.564980:0.350549:0.564980:0.350549:0.555425:0.345306:0.555425:0.000000
U:@0.507791:0.561816:0.518848:0.561816:0.518848:0.545455:0.507791:0.545455:0.000000
n:@0.518769:0.564980:0.524313:0.564980:0.524313:0.555441:0.518769:0.555441:0.000000
a r:@0.540825:0.561816:0.564449:0.561816:0.564449:0.545455:0.540825:0.545455:0.000000:0.000000:0.000000
n :@0.567207:0.555769:0.574631:0.555769:0.574631:0.546230:0.567207:0.546230:0.000000:0.000000
– 1:@0.574050:0.555769:0.586266:0.555769:0.586266:0.546214:0.574050:0.546214:0.000000:0.000000:0.000000
U:@0.668401:0.561816:0.678858:0.561816:0.678858:0.546423:0.668401:0.546423:0.000000
ar:@0.700929:0.561816:0.723009:0.561816:0.723009:0.546423:0.700929:0.546423:0.000000:0.000000
r:@0.809647:0.561816:0.814649:0.561816:0.814649:0.546423:0.809647:0.546423:0.000000
r:@0.845343:0.561816:0.850345:0.561816:0.850345:0.546423:0.845343:0.546423:0.000000
= ⋅:@0.688599:0.562494:0.684730:0.562494:0.684730:0.546921:0.688599:0.546921:0.000000:0.000000:0.000000
⇒:@0.742867:0.562494:0.715977:0.562494:0.715977:0.546921:0.742867:0.546921:0.000000
= ⋅⇒ =:@0.781276:0.562494:0.863619:0.562494:0.863619:0.546921:0.781276:0.546921:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
16 2:@0.761723:0.561816:0.801760:0.561816:0.801760:0.546146:0.761723:0.546146:0.000000:0.000000:0.000000:0.000000
2.:@0.866032:0.561816:0.877377:0.561816:0.877377:0.546146:0.866032:0.546146:0.000000:0.000000
4:@0.679046:0.563820:0.683975:0.563820:0.683975:0.554739:0.679046:0.554739:0.000000
4–1:@0.724839:0.554154:0.740119:0.554154:0.740119:0.545072:0.724839:0.545072:0.000000:0.000000:0.000000
3:@0.816081:0.554154:0.821009:0.554154:0.821009:0.545072:0.816081:0.545072:0.000000
   :@0.879969:0.561816:0.884005:0.561816:0.884005:0.545427:0.879969:0.545427:0.000000:0.000000:0.000000
Concluimos:@0.148521:0.578413:0.239203:0.578413:0.239203:0.561788:0.148521:0.561788:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 que la razón ( ) es dos (2).:@0.239203:0.578413:0.428730:0.578413:0.428730:0.562024:0.239203:0.562024:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r:@0.341972:0.578413:0.347261:0.578413:0.347261:0.562051:0.341972:0.562051:0.000000
b) :@0.115277:0.607691:0.135308:0.607691:0.135308:0.590791:0.115277:0.590791:0.000000:0.000000:0.000000
Una vez encontrado el valor de la razón, :@0.148521:0.607691:0.436735:0.607691:0.436735:0.591302:0.148521:0.591302:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
calculamos :@0.436397:0.607691:0.524371:0.607691:0.524371:0.591067:0.436397:0.591067:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la suma: :@0.524058:0.607691:0.586111:0.607691:0.586111:0.591302:0.524058:0.591302:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
= ⋅⎜:@0.607253:0.607144:0.644638:0.608480:0.644638:0.592907:0.607253:0.591571:0.000000:0.000000:0.000000:0.000000
−:@0.663310:0.598583:0.673427:0.598583:0.673427:0.583010:0.663310:0.583010:0.000000
− ⎠:@0.659385:0.618112:0.689451:0.619559:0.689451:0.603986:0.659385:0.602539:0.000000:0.000000:0.000000
⎛:@0.637548:0.595638:0.644625:0.595638:0.644625:0.580065:0.637548:0.580065:0.000000
⎝:@0.637562:0.619559:0.644638:0.619559:0.644638:0.603986:0.637562:0.603986:0.000000
⎞:@0.682378:0.595631:0.689454:0.595631:0.689454:0.580058:0.682378:0.580058:0.000000
⎟:@0.682375:0.608480:0.689451:0.608480:0.689451:0.592907:0.682375:0.592907:0.000000
1:@0.674101:0.597899:0.683093:0.597899:0.683093:0.581511:0.674101:0.581511:0.000000
1:@0.670175:0.617428:0.679168:0.617428:0.679168:0.601039:0.670175:0.601039:0.000000
S:@0.588762:0.606460:0.596833:0.606460:0.596833:0.590099:0.588762:0.590099:0.000000
a:@0.620697:0.606460:0.629966:0.606460:0.629966:0.590099:0.620697:0.590099:0.000000
r:@0.646975:0.597899:0.652264:0.597899:0.652264:0.581538:0.646975:0.581538:0.000000
r:@0.650900:0.617428:0.656189:0.617428:0.656189:0.601067:0.650900:0.601067:0.000000
n:@0.596783:0.608470:0.602294:0.608470:0.602294:0.598988:0.596783:0.598988:0.000000
n:@0.654005:0.590236:0.659515:0.590236:0.659515:0.580754:0.654005:0.580754:0.000000
 por lo que reemplazando :@0.694649:0.607686:0.884008:0.607686:0.884008:0.591297:0.694649:0.591297:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los valores: :@0.148528:0.634462:0.231839:0.634462:0.231839:0.618073:0.148528:0.618073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
= ⋅:@0.253505:0.634736:0.282086:0.634736:0.282086:0.619163:0.253505:0.619163:0.000000:0.000000:0.000000
⎛:@0.283450:0.625110:0.290526:0.625110:0.290526:0.609537:0.283450:0.609537:0.000000
⎝:@0.283450:0.645537:0.290526:0.645537:0.290526:0.629964:0.283450:0.629964:0.000000
⎜:@0.283450:0.639729:0.290526:0.639729:0.290526:0.624156:0.283450:0.624156:0.000000
⎞:@0.332394:0.625110:0.339470:0.625110:0.339470:0.609537:0.332394:0.609537:0.000000
⎠:@0.332394:0.645537:0.339470:0.645537:0.339470:0.629964:0.332394:0.629964:0.000000
⎟:@0.332394:0.639729:0.339470:0.639729:0.339470:0.624156:0.332394:0.624156:0.000000
=:@0.344648:0.634736:0.354765:0.634736:0.354765:0.619163:0.344648:0.619163:0.000000
2:@0.266902:0.634058:0.275894:0.634058:0.275894:0.618388:0.266902:0.618388:0.000000
2 –1:@0.294433:0.625096:0.333477:0.625096:0.333477:0.609426:0.294433:0.609426:0.000000:0.000000:0.000000:0.000000
2–1:@0.298524:0.644542:0.329454:0.644542:0.329454:0.628872:0.298524:0.628872:0.000000:0.000000:0.000000
30.:@0.358045:0.634058:0.378831:0.634058:0.378831:0.618388:0.358045:0.618388:0.000000:0.000000:0.000000
4:@0.243036:0.636062:0.248248:0.636062:0.248248:0.626981:0.243036:0.626981:0.000000
4:@0.303974:0.617434:0.309186:0.617434:0.309186:0.608353:0.303974:0.608353:0.000000
S:@0.234816:0.634058:0.242887:0.634058:0.242887:0.618665:0.234816:0.618665:0.000000
 :@0.148523:0.644558:0.152337:0.644558:0.152337:0.627657:0.148523:0.627657:0.000000
Concluimos:@0.148523:0.664722:0.239205:0.664722:0.239205:0.648098:0.148523:0.648098:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 que la suma de los primeros 4 términos de la progresión es igual a 30 (incluido  ).:@0.239205:0.664722:0.839111:0.664722:0.839111:0.648334:0.239205:0.648334:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.821752:0.664722:0.831021:0.664722:0.831021:0.648361:0.821752:0.648361:0.000000
Progresiones geométricas:@0.115891:0.141978:0.501011:0.141978:0.501011:0.101242:0.115891:0.101242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.54. Reconocer y calcular uno o varios parámetros de una progresión (aritmética o geométrica), conocidos otros parámetros. :@0.125388:0.069719:0.729377:0.069719:0.729377:0.059289:0.125388:0.059289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.56. Resolver ejercicios numéricos y problemas con la aplicación de las progresiones aritméticas, geométricas y sumas parciales finitas de sucesiones numéricas.:@0.125388:0.080280:0.875242:0.080280:0.875242:0.069851:0.125388:0.069851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
15:@0.048404:0.122645:0.082107:0.122645:0.082107:0.065614:0.048404:0.065614:0.000000:0.000000
Progresiones geométricas:@0.394496:0.169495:0.600757:0.169495:0.600757:0.152595:0.394496:0.152595:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.122468:0.210765:0.204047:0.210765:0.204047:0.193864:0.122468:0.193864:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sucesión cuyos términos son tales que cada uno de ellos (a partir del segun-:@0.308163:0.194169:0.872692:0.194169:0.872692:0.177780:0.308163:0.177780:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
do) es igual al término precedente multiplicado por un número fijo que se :@0.308163:0.210765:0.876814:0.210765:0.876814:0.194376:0.308163:0.194376:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
llama razón y se expresa con la letra  .:@0.308163:0.227362:0.582197:0.227362:0.582197:0.210973:0.308163:0.210973:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r:@0.573701:0.227362:0.578990:0.227362:0.578990:0.211000:0.573701:0.211000:0.000000
Razón:@0.122468:0.268963:0.171596:0.268963:0.171596:0.252062:0.122468:0.252062:0.000000:0.000000:0.000000:0.000000:0.000000
Si la razón es r > 1, la progresión es creciente y decreciente cuando 0 <   < 1.:@0.308163:0.250583:0.865593:0.250583:0.865593:0.234194:0.308163:0.234194:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r:@0.829051:0.250583:0.834340:0.250583:0.834340:0.234221:0.829051:0.234221:0.000000
•  Se calcula diviendo un término por el que le precede.:@0.308163:0.268963:0.714264:0.268963:0.714264:0.252574:0.308163:0.252574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•  La razón puede ser un número positivo o negativo.:@0.308163:0.287344:0.696078:0.287344:0.696078:0.270955:0.308163:0.270955:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Notación y término :@0.122468:0.309666:0.279432:0.309666:0.279432:0.292765:0.122468:0.292765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n-ésimo:@0.122468:0.326262:0.187056:0.326262:0.187056:0.309361:0.122468:0.309361:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.308163:0.308781:0.317432:0.308781:0.317432:0.292419:0.308163:0.292419:0.000000
 = primer término;   = razón o diferencia;    = número de términos:@0.317432:0.308781:0.801541:0.308781:0.801541:0.292392:0.317432:0.292392:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r:@0.455527:0.308781:0.460816:0.308781:0.460816:0.292419:0.455527:0.292419:0.000000
n:@0.621634:0.308781:0.631142:0.308781:0.631142:0.292419:0.621634:0.292419:0.000000
Término n-ésimo :@0.308163:0.327161:0.437007:0.327161:0.437007:0.310772:0.308163:0.310772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Un:@0.437007:0.327161:0.457572:0.327161:0.457572:0.310800:0.437007:0.310800:0.000000:0.000000
 = a • :@0.457572:0.327161:0.497616:0.327161:0.497616:0.310772:0.457572:0.310772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r :@0.497616:0.327161:0.506221:0.327161:0.506221:0.310800:0.497616:0.310800:0.000000:0.000000
n – :@0.506221:0.321111:0.521004:0.321111:0.521004:0.311573:0.506221:0.311573:0.000000:0.000000:0.000000:0.000000
1:@0.521004:0.321111:0.526247:0.321111:0.526247:0.311556:0.521004:0.311556:0.000000
, el último término:   = :@0.526246:0.327159:0.691337:0.327159:0.691337:0.310770:0.526246:0.310770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
l:@0.668487:0.327159:0.672283:0.327159:0.672283:0.310797:0.668487:0.310797:0.000000
ar :@0.691337:0.327159:0.709212:0.327159:0.709212:0.310797:0.691337:0.310797:0.000000:0.000000:0.000000
n:@0.709210:0.321111:0.714754:0.321111:0.714754:0.311573:0.709210:0.311573:0.000000
–1:@0.714754:0.321111:0.725368:0.321111:0.725368:0.311556:0.714754:0.311556:0.000000:0.000000
Suma de los primeros  :@0.122474:0.353192:0.298016:0.353192:0.298016:0.336292:0.122474:0.336292:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
términos:@0.122474:0.369789:0.193863:0.369789:0.193863:0.352888:0.122474:0.352888:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
= ⋅:@0.329420:0.358816:0.359107:0.358816:0.359107:0.343243:0.329420:0.343243:0.000000:0.000000:0.000000
⎛:@0.360464:0.349190:0.367540:0.349190:0.367540:0.333617:0.360464:0.333617:0.000000
⎝:@0.360464:0.369623:0.367540:0.369623:0.367540:0.354050:0.360464:0.354050:0.000000
⎜:@0.360464:0.363814:0.367540:0.363814:0.367540:0.348241:0.360464:0.348241:0.000000
⎞:@0.407057:0.349190:0.414133:0.349190:0.414133:0.333617:0.407057:0.333617:0.000000
⎠:@0.407057:0.369623:0.414133:0.369623:0.414133:0.354050:0.407057:0.354050:0.000000
⎟:@0.407057:0.363814:0.414133:0.363814:0.414133:0.348241:0.407057:0.348241:0.000000
=:@0.439453:0.358821:0.449570:0.358821:0.449570:0.343248:0.439453:0.343248:0.000000
–1:@0.388576:0.349180:0.408146:0.349180:0.408146:0.332791:0.388576:0.332791:0.000000:0.000000
–1:@0.384703:0.368631:0.404273:0.368631:0.404273:0.352242:0.384703:0.352242:0.000000:0.000000
;:@0.417744:0.358147:0.420950:0.358147:0.420950:0.341758:0.417744:0.341758:0.000000
,:@0.422664:0.358147:0.425870:0.358147:0.425870:0.341758:0.422664:0.341758:0.000000
–:@0.466840:0.349183:0.476054:0.349183:0.476054:0.332794:0.466840:0.332794:0.000000
–1:@0.467781:0.368632:0.487352:0.368632:0.487352:0.352243:0.467781:0.352243:0.000000:0.000000
S:@0.311146:0.358148:0.319218:0.358148:0.319218:0.341787:0.311146:0.341787:0.000000
a:@0.343192:0.358148:0.352461:0.358148:0.352461:0.341787:0.343192:0.341787:0.000000
r:@0.371822:0.349184:0.377111:0.349184:0.377111:0.332823:0.371822:0.332823:0.000000
r:@0.375643:0.368633:0.380932:0.368633:0.380932:0.352272:0.375643:0.352272:0.000000
S:@0.427572:0.358150:0.435644:0.358150:0.435644:0.341788:0.427572:0.341788:0.000000
lr a:@0.454328:0.349185:0.488201:0.349185:0.488201:0.332824:0.454328:0.332824:0.000000:0.000000:0.000000:0.000000
r:@0.458723:0.368634:0.464012:0.368634:0.464012:0.352273:0.458723:0.352273:0.000000
n:@0.319159:0.360142:0.324670:0.360142:0.324670:0.350660:0.319159:0.350660:0.000000
n:@0.378838:0.341519:0.384349:0.341519:0.384349:0.332037:0.378838:0.332037:0.000000
..:@0.524755:0.372679:0.531002:0.372679:0.531002:0.357009:0.524755:0.357009:0.000000:0.000000
Aplicación de  :@0.122474:0.412735:0.237555:0.412735:0.237555:0.395835:0.122474:0.395835:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
progresiones en  :@0.122474:0.429332:0.258452:0.429332:0.258452:0.412431:0.122474:0.412431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
finanzas: Valor futuro:@0.122474:0.445928:0.291399:0.445928:0.291399:0.429028:0.122474:0.429028:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.458098:0.405986:0.464235:0.405986:0.464235:0.386053:0.458098:0.386053:0.000000
):@0.490605:0.405986:0.496741:0.405986:0.496741:0.386053:0.490605:0.386053:0.000000
(:@0.531182:0.405986:0.537319:0.405986:0.537319:0.386053:0.531182:0.386053:0.000000
):@0.563689:0.405986:0.569825:0.405986:0.569825:0.386053:0.563689:0.386053:0.000000
=:@0.335126:0.403532:0.345243:0.403532:0.345243:0.387959:0.335126:0.387959:0.000000
+:@0.380145:0.403532:0.390261:0.403532:0.390261:0.387959:0.380145:0.387959:0.000000
=:@0.413701:0.403532:0.423818:0.403532:0.423818:0.387959:0.413701:0.387959:0.000000
+ =:@0.471232:0.403532:0.509520:0.403532:0.509520:0.387959:0.471232:0.387959:0.000000:0.000000:0.000000
+:@0.544330:0.403532:0.554447:0.403532:0.554447:0.387959:0.544330:0.387959:0.000000
VF:@0.309997:0.402854:0.326840:0.402854:0.326840:0.386493:0.309997:0.386493:0.000000:0.000000
VF:@0.347018:0.402854:0.363861:0.402854:0.363861:0.386493:0.347018:0.386493:0.000000:0.000000
VF:@0.425594:0.402854:0.442437:0.402854:0.442437:0.386493:0.425594:0.386493:0.000000:0.000000
r:@0.483751:0.402854:0.489040:0.402854:0.489040:0.386493:0.483751:0.386493:0.000000
VP:@0.511282:0.402854:0.528854:0.402854:0.528854:0.386493:0.511282:0.386493:0.000000:0.000000
r:@0.556827:0.402854:0.562116:0.402854:0.562116:0.386493:0.556827:0.386493:0.000000
n:@0.325232:0.404858:0.330743:0.404858:0.330743:0.395376:0.325232:0.395376:0.000000
n:@0.362248:0.404858:0.367758:0.404858:0.367758:0.395376:0.362248:0.395376:0.000000
n:@0.440828:0.404858:0.446339:0.404858:0.446339:0.395376:0.440828:0.395376:0.000000
n:@0.570298:0.393308:0.575809:0.393308:0.575809:0.383826:0.570298:0.383826:0.000000
int:@0.391875:0.402854:0.410966:0.402854:0.410966:0.386465:0.391875:0.386465:0.000000:0.000000:0.000000
1:@0.463374:0.402854:0.472367:0.402854:0.472367:0.386465:0.463374:0.386465:0.000000
1:@0.536458:0.402854:0.545451:0.402854:0.545451:0.386465:0.536458:0.386465:0.000000
–1:@0.367950:0.404858:0.378192:0.404858:0.378192:0.395360:0.367950:0.395360:0.000000:0.000000
–1:@0.446531:0.404858:0.456773:0.404858:0.456773:0.395360:0.446531:0.395360:0.000000:0.000000
(:@0.345596:0.458432:0.351732:0.458432:0.351732:0.438499:0.345596:0.438499:0.000000
):@0.378102:0.458432:0.384239:0.458432:0.384239:0.438499:0.378102:0.438499:0.000000
=:@0.331460:0.443601:0.341577:0.443601:0.341577:0.428028:0.331460:0.428028:0.000000
+:@0.358733:0.455979:0.368850:0.455979:0.368850:0.440406:0.358733:0.440406:0.000000
VP:@0.309992:0.442923:0.327554:0.442923:0.327554:0.426562:0.309992:0.426562:0.000000:0.000000
VF:@0.357167:0.434404:0.374010:0.434404:0.374010:0.418043:0.357167:0.418043:0.000000:0.000000
r:@0.371246:0.455301:0.376534:0.455301:0.376534:0.438940:0.371246:0.438940:0.000000
n:@0.372400:0.436401:0.377911:0.436401:0.377911:0.426919:0.372400:0.426919:0.000000
n:@0.384703:0.445755:0.390214:0.445755:0.390214:0.436273:0.384703:0.436273:0.000000
1:@0.350883:0.455300:0.359876:0.455300:0.359876:0.438911:0.350883:0.438911:0.000000
=:@0.502913:0.437668:0.513030:0.437668:0.513030:0.422095:0.502913:0.422095:0.000000
=:@0.502494:0.458413:0.512611:0.458413:0.512611:0.442840:0.502494:0.442840:0.000000
Valor presente o actual:@0.517052:0.436990:0.686660:0.436990:0.686660:0.420601:0.517052:0.420601:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
..:@0.553078:0.436990:0.559325:0.436990:0.559325:0.420601:0.553078:0.420601:0.000000:0.000000
.. ..:@0.622237:0.436990:0.644147:0.436990:0.644147:0.420601:0.622237:0.420601:0.000000:0.000000:0.000000:0.000000:0.000000
Valor final o futuro:@0.516646:0.457736:0.654596:0.457736:0.654596:0.441347:0.516646:0.441347:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
..:@0.552672:0.457736:0.558919:0.457736:0.558919:0.441347:0.552672:0.441347:0.000000:0.000000
.. ..:@0.588625:0.457736:0.610535:0.457736:0.610535:0.441347:0.588625:0.441347:0.000000:0.000000:0.000000:0.000000:0.000000
VP:@0.481100:0.436990:0.498661:0.436990:0.498661:0.420629:0.481100:0.420629:0.000000:0.000000
VF:@0.481100:0.457736:0.497942:0.457736:0.497942:0.441374:0.481100:0.441374:0.000000:0.000000
Donde::@0.415769:0.444911:0.469651:0.444911:0.469651:0.428522:0.415769:0.428522:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.148457:0.828993:0.167180:0.828993:0.167180:0.812092:0.148457:0.812092:0.000000:0.000000:0.000000
La razón  .:@0.181701:0.828993:0.255651:0.828993:0.255651:0.812604:0.181701:0.812604:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r:@0.247156:0.828993:0.252444:0.828993:0.252444:0.812631:0.247156:0.812631:0.000000
 :@0.148457:0.925763:0.152272:0.925763:0.152272:0.908863:0.148457:0.908863:0.000000
b) :@0.540917:0.828994:0.560948:0.828994:0.560948:0.812093:0.540917:0.812093:0.000000:0.000000:0.000000
El primer término de la progresión.:@0.574161:0.828994:0.834914:0.828994:0.834914:0.812605:0.574161:0.812605:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.540917:0.925765:0.544732:0.925765:0.544732:0.908864:0.540917:0.908864:0.000000
r:@0.212281:0.879209:0.217569:0.879209:0.217569:0.862848:0.212281:0.862848:0.000000
 = 2:@0.217569:0.879209:0.245616:0.879209:0.245616:0.862820:0.217569:0.862820:0.000000:0.000000:0.000000:0.000000
a :@0.606429:0.879209:0.619015:0.879209:0.619015:0.862848:0.606429:0.862848:0.000000:0.000000
= 2:@0.619015:0.879209:0.643027:0.879209:0.643027:0.862820:0.619015:0.862820:0.000000:0.000000:0.000000