Question

calcular a12 de uma p.a que a5=4 e a15=8​

Answer 1

Vamos começar determinando a razão utilizando a equação do termo geral da PA:

$a_n~=~a_m+(n-m).r\\\\\\\\a_{15}~=~a_5+(15-5).r\\\\\\8~=~4+10r\\\\\\10r~=~8-4\\\\\\r~=~\frac{4}{10}\\\\\\\boxed{r~=~\frac{2}{5}}$

Agora, novamente utilizando a equação do termo geral, podemos determinar o valor de a12:

$a_{12}~=~a_5+(12-5).r\\\\\\a_{12}~=~4~+~7~.~\frac{2}{5}\\\\\\a_{12}~=~4+\frac{14}{5}\\\\\\a_{12}~=~\frac{5~.~4~+~1~.~14}{5}\\\\\\\boxed{a_{12}~=~\frac{34}{5}~~ou~~6,8}$