Question

continuando a sequencia 2,6,18 encontraremos que número na oitava posição?

Answer 1

$\mathbf{Perceba\ que\ a\ sequ\hat{e}ncia\ forma\ uma\ progress\~ao}\\ \mathbf{geom\acute{e}trica\ (PG)\ de\ raz\~ao\ igual\ a\ 3:}\\\\ \boxed{\mathrm{PG=\{a_1;a_2;a_3;\dots\}=\{2;6;18;\dots\}}}\ \to\ \boxed{\mathrm{q=3}}\\\\ \mathbf{Para\ encontrarmos\ o\ oitavo\ termo,\ devemos}\\ \mathbf{utilizar\ o\ termo\ geral\ de\ uma\ PG:}\\\\ \boxed{\mathrm{a_n=a_1.q^{n-1}}}\ \to\ \mathrm{a_8=a_1.q^{8-1}\ \to\ a_8=a_1.q^7}\\\\ \mathrm{a_8=2.3^7\ \to\ a_8=2.2187\ \to\ \boxed{\mathrm{a_8=4374}}}\\\\ \mathbf{Portanto,\ o\ n\acute{u}mero\ na\ oitava\ posi\c{c}\~ao\ da}\\ \mathbf{sequ\hat{e}ncia\ \acute{e}\ o\ 4374.}$