64:@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
Taller:@0.175844:0.743997:0.236739:0.743997:0.236739:0.710049:0.175844:0.710049:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
I.M.5.4.1. Identifica las sucesiones según sus características y halla los parámetros desconocidos; aplica progresiones en aplicaciones :@0.256865:0.721462:0.877758:0.721462:0.877758:0.711033:0.256865:0.711033:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cotidianas y analiza el sistema financiero local, apreciando la importancia de estos conocimientos para la toma de decisiones asertivas. :@0.256865:0.732023:0.877740:0.732023:0.877740:0.721594:0.256865:0.721594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(J.2.):@0.256865:0.742585:0.277000:0.742585:0.277000:0.732155:0.256865:0.732155:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1. :@0.115209:0.782720:0.133950:0.782720:0.133950:0.765584:0.115209:0.765584:0.000000:0.000000:0.000000
El cuarto término de una progresión aritmética es 16 y el octavo término es 32.:@0.148452:0.782720:0.724699:0.782720:0.724699:0.766331:0.148452:0.766331:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.148452:0.809745:0.167175:0.809745:0.167175:0.792844:0.148452:0.792844:0.000000:0.000000:0.000000
Halla:@0.181696:0.809745:0.220173:0.809745:0.220173:0.793121:0.181696:0.793121:0.000000:0.000000:0.000000:0.000000:0.000000
 la diferencia  .:@0.220173:0.809745:0.328876:0.809745:0.328876:0.793356:0.220173:0.793356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.316400:0.809745:0.325669:0.809745:0.325669:0.793383:0.316400:0.793383:0.000000
 :@0.148452:0.906515:0.152267:0.906515:0.152267:0.889615:0.148452:0.889615:0.000000
b) :@0.540917:0.809747:0.560948:0.809747:0.560948:0.792846:0.540917:0.792846:0.000000:0.000000:0.000000
Encuentra:@0.574161:0.809747:0.653639:0.809747:0.653639:0.793123:0.574161:0.793123:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 el primer término de la  :@0.653823:0.809747:0.838524:0.809747:0.838524:0.793358:0.653823:0.793358:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
progresión.:@0.574161:0.826343:0.658873:0.826343:0.658873:0.809955:0.574161:0.809955:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.540917:0.923114:0.544732:0.923114:0.544732:0.906214:0.540917:0.906214:0.000000
Actividad resuelta:@0.115209:0.478875:0.272331:0.478875:0.272331:0.460437:0.115209:0.460437:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El primer término de una progresión aritmética es 1 y el décimo quinto es 29. :@0.115209:0.498721:0.691294:0.498721:0.691294:0.482332:0.115209:0.482332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Hallamos:@0.691828:0.498721:0.763088:0.498721:0.763088:0.482097:0.691828:0.482097:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la diferencia ( ) :@0.763088:0.498721:0.883991:0.498721:0.883991:0.482332:0.763088:0.482332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.865803:0.498721:0.875073:0.498721:0.875073:0.482360:0.865803:0.482360:0.000000
 :@0.879901:0.498721:0.883936:0.498721:0.883936:0.482332:0.879901:0.482332:0.000000
y la suma de los quince primeros términos.:@0.115209:0.515317:0.428271:0.515317:0.428271:0.498928:0.115209:0.498928:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.115209:0.539036:0.133931:0.539036:0.133931:0.522136:0.115209:0.522136:0.000000:0.000000:0.000000
Sabemos:@0.148452:0.539036:0.218975:0.539036:0.218975:0.522412:0.148452:0.522412:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 que   = 1 y que :@0.218975:0.539036:0.341998:0.539036:0.341998:0.522647:0.218975:0.522647:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.255757:0.539036:0.265026:0.539036:0.265026:0.522675:0.255757:0.522675:0.000000
u:@0.341998:0.539036:0.351322:0.539036:0.351322:0.522675:0.341998:0.522675:0.000000
15:@0.351315:0.542205:0.361801:0.542205:0.361801:0.532650:0.351315:0.532650:0.000000:0.000000
 = 29;   = 15. Por el cálculo del n-ésimo término   =   + (  – 1)d,  :@0.361801:0.539041:0.843913:0.539041:0.843913:0.522652:0.361801:0.522652:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.406082:0.539041:0.415591:0.539041:0.415591:0.522680:0.406082:0.522680:0.000000
u:@0.715022:0.539041:0.724346:0.539041:0.724346:0.522680:0.715022:0.522680:0.000000
n:@0.724339:0.542205:0.729883:0.542205:0.729883:0.532667:0.724339:0.532667:0.000000
a:@0.748937:0.539041:0.758206:0.539041:0.758206:0.522680:0.748937:0.522680:0.000000
n:@0.782143:0.539041:0.791652:0.539041:0.791652:0.522680:0.782143:0.522680:0.000000
tenemos: :@0.148454:0.559455:0.220801:0.559455:0.220801:0.543066:0.148454:0.543066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.279900:0.561813:0.243210:0.561813:0.243210:0.541413:0.279900:0.541413:0.000000
):@0.322726:0.561813:0.286036:0.561813:0.286036:0.541413:0.322726:0.541413:0.000000
=+:@0.246553:0.559942:0.277566:0.559942:0.277566:0.544369:0.246553:0.544369:0.000000:0.000000
⇒:@0.342984:0.559942:0.361172:0.559942:0.361172:0.544369:0.342984:0.544369:0.000000
=+:@0.384760:0.559942:0.415774:0.559942:0.415774:0.544369:0.384760:0.544369:0.000000:0.000000
⇒ =:@0.449091:0.559942:0.493704:0.559942:0.493704:0.544369:0.449091:0.544369:0.000000:0.000000:0.000000
1 15–1:@0.258789:0.559264:0.324892:0.559264:0.324892:0.543594:0.258789:0.543594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
29 1 14:@0.363695:0.559264:0.435134:0.559264:0.435134:0.543594:0.363695:0.543594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.:@0.496973:0.559264:0.508969:0.559264:0.508969:0.543594:0.496973:0.543594:0.000000:0.000000
15:@0.231631:0.561268:0.241921:0.561268:0.241921:0.552186:0.231631:0.552186:0.000000:0.000000
u:@0.223412:0.559264:0.232737:0.559264:0.232737:0.543871:0.223412:0.543871:0.000000
d:@0.329946:0.559264:0.339215:0.559264:0.339215:0.543871:0.329946:0.543871:0.000000
d:@0.436062:0.559264:0.445331:0.559264:0.445331:0.543871:0.436062:0.543871:0.000000
d:@0.470190:0.559264:0.479459:0.559264:0.479459:0.543871:0.470190:0.543871:0.000000
 :@0.115209:0.579612:0.119023:0.579612:0.119023:0.562711:0.115209:0.562711:0.000000
Concluimos:@0.148452:0.579612:0.239135:0.579612:0.239135:0.562988:0.148452:0.562988:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 que la diferencia ( ) es dos (2).:@0.239135:0.579612:0.463731:0.579612:0.463731:0.563223:0.239135:0.563223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.372993:0.579612:0.382262:0.579612:0.382262:0.563251:0.372993:0.563251:0.000000
b) :@0.115209:0.599777:0.135240:0.599777:0.135240:0.582876:0.115209:0.582876:0.000000:0.000000:0.000000
Una vez encontrado el valor de la diferencia, :@0.148452:0.599777:0.467803:0.599777:0.467803:0.583388:0.148452:0.583388:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
encontramos :@0.467619:0.599777:0.571072:0.599777:0.571072:0.583153:0.467619:0.583153:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la suma de los quince primeros términos: :@0.570888:0.599777:0.868861:0.599777:0.868861:0.583388:0.570888:0.583388:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.115209:0.629650:0.119023:0.629650:0.119023:0.612749:0.115209:0.612749:0.000000
(:@0.207607:0.633117:0.213743:0.633117:0.213743:0.610692:0.207607:0.610692:0.000000
):@0.300482:0.633117:0.306618:0.633117:0.306618:0.610692:0.300482:0.610692:0.000000
(:@0.246661:0.631867:0.252798:0.631867:0.252798:0.611933:0.246661:0.611933:0.000000
):@0.282208:0.631867:0.288345:0.631867:0.288345:0.611933:0.282208:0.611933:0.000000
=:@0.171380:0.629411:0.181496:0.629411:0.181496:0.613838:0.171380:0.613838:0.000000
+:@0.234513:0.629411:0.244629:0.629411:0.244629:0.613838:0.234513:0.613838:0.000000
1:@0.186306:0.620214:0.195299:0.620214:0.195299:0.603825:0.186306:0.603825:0.000000
2:@0.185515:0.639657:0.194508:0.639657:0.194508:0.623268:0.185515:0.623268:0.000000
2:@0.214041:0.628731:0.223034:0.628731:0.223034:0.612342:0.214041:0.612342:0.000000
–1:@0.265196:0.628731:0.284748:0.628731:0.284748:0.612342:0.265196:0.612342:0.000000:0.000000
, por lo que reemplazando los valores::@0.308059:0.628731:0.585264:0.629641:0.585264:0.613252:0.308059:0.612342:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sn:@0.151434:0.628733:0.168996:0.628733:0.168996:0.612372:0.151434:0.612372:0.000000:0.000000
na:@0.197301:0.628733:0.232479:0.628733:0.232479:0.612372:0.197301:0.612372:0.000000:0.000000
n:@0.253466:0.628733:0.262975:0.628733:0.262975:0.612372:0.253466:0.612372:0.000000
d:@0.289806:0.628733:0.299075:0.628733:0.299075:0.612372:0.289806:0.612372:0.000000
 :@0.312056:0.629641:0.315871:0.629641:0.315871:0.612741:0.312056:0.612741:0.000000
 :@0.148456:0.664134:0.152270:0.664134:0.152270:0.647233:0.148456:0.647233:0.000000
 :@0.181699:0.664134:0.185514:0.664134:0.185514:0.647233:0.181699:0.647233:0.000000
() (:@0.258954:0.667265:0.296808:0.667265:0.296808:0.647331:0.258954:0.647331:0.000000:0.000000:0.000000:0.000000
):@0.332709:0.667265:0.338846:0.667265:0.338846:0.647331:0.332709:0.647331:0.000000
( ):@0.417257:0.667265:0.447370:0.667265:0.447370:0.647331:0.417257:0.647331:0.000000:0.000000:0.000000
=:@0.210163:0.664810:0.151895:0.664810:0.151895:0.649238:0.210163:0.649238:0.000000
+:@0.278537:0.664810:0.220269:0.664810:0.220269:0.649238:0.278537:0.649238:0.000000
⎡:@0.242153:0.662722:0.249230:0.662722:0.249230:0.647149:0.242153:0.647149:0.000000
⎣:@0.242153:0.667521:0.249230:0.667521:0.249230:0.651948:0.242153:0.651948:0.000000
⎤ =:@0.348684:0.662722:0.337111:0.664810:0.337111:0.649238:0.348684:0.647149:0.000000:0.000000:0.000000
⎦:@0.348684:0.667521:0.355760:0.667521:0.355760:0.651948:0.348684:0.651948:0.000000
+:@0.387953:0.664810:0.367590:0.664810:0.367590:0.649238:0.387953:0.649238:0.000000
=:@0.450045:0.664810:0.429682:0.664810:0.429682:0.649238:0.450045:0.649238:0.000000
15:@0.223136:0.655613:0.240919:0.655613:0.240919:0.639944:0.223136:0.639944:0.000000:0.000000
2:@0.227909:0.675055:0.236902:0.675055:0.236902:0.659385:0.227909:0.659385:0.000000
2 1:@0.249007:0.664132:0.273234:0.664132:0.273234:0.648462:0.249007:0.648462:0.000000:0.000000:0.000000
15–1 2:@0.295966:0.664132:0.348929:0.664132:0.348929:0.648462:0.295966:0.648462:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
15 15 14:@0.368993:0.664132:0.440321:0.664132:0.440321:0.648462:0.368993:0.648462:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
225.:@0.462686:0.664132:0.492263:0.664132:0.492263:0.648462:0.462686:0.648462:0.000000:0.000000:0.000000:0.000000
15:@0.195609:0.666137:0.205898:0.666137:0.205898:0.657055:0.195609:0.657055:0.000000:0.000000
S:@0.188489:0.664133:0.196560:0.664133:0.196560:0.648740:0.188489:0.648740:0.000000
         :@0.115209:0.691434:0.151530:0.691434:0.151530:0.675045:0.115209:0.675045:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Concluimos:@0.151530:0.691434:0.242214:0.691434:0.242214:0.674810:0.151530:0.674810:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 que la suma de los primeros 15 términos de la progresión aritmética es igual a 225.:@0.242214:0.691434:0.851352:0.691434:0.851352:0.675045:0.242214:0.675045:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Progresiones aritméticas:@0.115891:0.141978:0.487090:0.141978:0.487090:0.101242:0.115891:0.101242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
14:@0.048229:0.122645:0.082283:0.122645:0.082283:0.065614:0.048229:0.065614:0.000000:0.000000
M.5.1.54. Reconocer y calcular uno o varios parámetros de una progresión (aritmética o geométrica), conocidos otros parámetros.  :@0.125388:0.066250:0.731945:0.066250:0.731945:0.055820:0.125388:0.055820:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.56. Resolver ejercicios numéricos y problemas con la aplicación de las progresiones aritméticas, geométricas y sumas parciales finitas de sucesiones :@0.125388:0.076811:0.839851:0.076811:0.839851:0.066382:0.125388:0.066382:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
numéricas.:@0.125388:0.087372:0.176022:0.087372:0.176022:0.076943:0.125388:0.076943:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Progresiones aritméticas:@0.399453:0.166981:0.595800:0.166981:0.595800:0.150080:0.399453:0.150080:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.122468:0.212178:0.204047:0.212178:0.204047:0.195278:0.122468:0.195278:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sucesión cuyos términos son tales que cada uno de ellos (a par-:@0.407930:0.195582:0.872786:0.195582:0.872786:0.179193:0.407930:0.179193:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tir del segundo) es igual al término precedente aumentado en :@0.407930:0.212178:0.876819:0.212178:0.876819:0.195789:0.407930:0.195789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un número fijo que se llama diferencia y se expresa con la letra  .:@0.407930:0.228775:0.872730:0.228775:0.872730:0.212386:0.407930:0.212386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.860255:0.228775:0.869524:0.228775:0.869524:0.212413:0.860255:0.212413:0.000000
Diferencia:@0.122468:0.285894:0.203807:0.285894:0.203807:0.268993:0.122468:0.268993:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•  La diferencia   puede ser positiva, negativa o nula. Si es po-:@0.407930:0.257431:0.872767:0.257431:0.872767:0.241042:0.407930:0.241042:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.522456:0.257431:0.531725:0.257431:0.531725:0.241070:0.522456:0.241070:0.000000
sitiva la progresión es creciente, y decreciente cuando   es :@0.423004:0.274027:0.876803:0.274027:0.876803:0.257639:0.423004:0.257639:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.841219:0.274027:0.850488:0.274027:0.850488:0.257666:0.841219:0.257666:0.000000
negativa.:@0.423004:0.290624:0.489657:0.290624:0.489657:0.274235:0.423004:0.274235:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•  Se calcula restando dos términos consecutivos.:@0.407930:0.314343:0.767761:0.314343:0.767761:0.297954:0.407930:0.297954:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Notación y término n-simo:@0.122468:0.355668:0.334199:0.355668:0.334199:0.338767:0.122468:0.338767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.407930:0.343801:0.417199:0.343801:0.417199:0.327440:0.407930:0.327440:0.000000
 = primer término;   = diferencia:@0.417199:0.343801:0.655467:0.343801:0.655467:0.327412:0.417199:0.327412:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.555294:0.343801:0.564563:0.343801:0.564563:0.327440:0.555294:0.327440:0.000000
Término n-ésimo:   = a + (  – 1):@0.407930:0.367520:0.646873:0.367543:0.646873:0.351154:0.407930:0.351131:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.539981:0.367520:0.549305:0.367520:0.549305:0.351159:0.539981:0.351159:0.000000
n:@0.549302:0.370707:0.554845:0.370707:0.554845:0.361168:0.549302:0.361168:0.000000
n:@0.606203:0.367543:0.615712:0.367543:0.615712:0.351182:0.606203:0.351182:0.000000
d   :@0.646873:0.367543:0.666093:0.367543:0.666093:0.351182:0.646873:0.351182:0.000000:0.000000:0.000000:0.000000
o   l =   + (  – 1):@0.666093:0.367543:0.784841:0.367543:0.784841:0.351154:0.666093:0.351154:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.710964:0.367543:0.720233:0.367543:0.720233:0.351182:0.710964:0.351182:0.000000
n:@0.744171:0.367543:0.753679:0.367543:0.753679:0.351182:0.744171:0.351182:0.000000
d:@0.784841:0.367543:0.794110:0.367543:0.794110:0.351182:0.784841:0.351182:0.000000
Suma de los n primeros términos:@0.122478:0.420568:0.383207:0.420568:0.383207:0.403668:0.122478:0.403668:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Se calcula con la siguiente fórmula::@0.407940:0.402395:0.664633:0.402395:0.664633:0.386006:0.407940:0.386006:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.465042:0.440306:0.471179:0.440306:0.471179:0.417881:0.465042:0.417881:0.000000
):@0.557918:0.440306:0.564054:0.440306:0.564054:0.417881:0.557918:0.417881:0.000000
(:@0.504097:0.439054:0.510234:0.439054:0.510234:0.419121:0.504097:0.419121:0.000000
):@0.539644:0.439054:0.545781:0.439054:0.545781:0.419121:0.539644:0.419121:0.000000
=:@0.428815:0.436600:0.438932:0.436600:0.438932:0.421027:0.428815:0.421027:0.000000
+:@0.491948:0.436600:0.502065:0.436600:0.502065:0.421027:0.491948:0.421027:0.000000
1:@0.443742:0.427403:0.452734:0.427403:0.452734:0.411014:0.443742:0.411014:0.000000
2:@0.442951:0.446845:0.451944:0.446845:0.451944:0.430456:0.442951:0.430456:0.000000
2:@0.471477:0.435919:0.480470:0.435919:0.480470:0.419530:0.471477:0.419530:0.000000
–1:@0.522632:0.435919:0.542197:0.435923:0.542197:0.419534:0.522632:0.419530:0.000000:0.000000
S:@0.410919:0.435923:0.418990:0.435923:0.418990:0.419561:0.410919:0.419561:0.000000
n a:@0.454740:0.435923:0.489918:0.435923:0.489918:0.419561:0.454740:0.419561:0.000000:0.000000:0.000000
n:@0.510907:0.435923:0.520416:0.435923:0.520416:0.419561:0.510907:0.419561:0.000000
d:@0.547246:0.435923:0.556515:0.435923:0.556515:0.419561:0.547246:0.419561:0.000000
n:@0.418921:0.437926:0.424432:0.437926:0.424432:0.428444:0.418921:0.428444:0.000000
 que es equivalente a :@0.567075:0.435494:0.726636:0.435494:0.726636:0.419105:0.567075:0.419105:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.729620:0.434917:0.737691:0.434917:0.737691:0.418555:0.729620:0.418555:0.000000
n:@0.762034:0.426397:0.771543:0.426397:0.771543:0.410036:0.762034:0.410036:0.000000
al:@0.780611:0.434917:0.807865:0.434917:0.807865:0.418555:0.780611:0.418555:0.000000:0.000000
n:@0.737631:0.436921:0.743141:0.436921:0.743141:0.427438:0.737631:0.427438:0.000000
(:@0.773804:0.438049:0.779941:0.438049:0.779941:0.418115:0.773804:0.418115:0.000000
):@0.809351:0.438049:0.815487:0.438049:0.815487:0.418115:0.809351:0.418115:0.000000
=:@0.747525:0.435594:0.757641:0.435594:0.757641:0.420022:0.747525:0.420022:0.000000
+:@0.791917:0.435594:0.802034:0.435594:0.802034:0.420022:0.791917:0.420022:0.000000
2:@0.762027:0.445843:0.771020:0.445843:0.771020:0.429454:0.762027:0.429454:0.000000
d:@0.214628:0.860400:0.223897:0.860400:0.223897:0.844039:0.214628:0.844039:0.000000
 = 4:@0.223897:0.860400:0.251943:0.860400:0.251943:0.844011:0.223897:0.844011:0.000000:0.000000:0.000000:0.000000
a:@0.604980:0.877176:0.614249:0.877176:0.614249:0.860815:0.604980:0.860815:0.000000
 = 4:@0.614249:0.877176:0.642296:0.877176:0.642296:0.860787:0.614249:0.860787:0.000000:0.000000:0.000000:0.000000