Question

Determine o numero de termos da PA (-3, 1, 5, ..., 113)

Answer 1

Vamos começar determinando a razão (r) da PA:

$\boxed{r~=~a_{n-1}-a_n}\\\\\\r~=~a_2-a_1\\\\\\r~=~1-(-3)\\\\\\r~=~1+3\\\\\\\boxed{r~=~4}$

Podemos agora determinar o numero de "n" de termos da PA utilizando a relação do termo geral da PA:

$\boxed{a_n~=~a_m~+~(n-m)\cdot r}\\\\\\a_n~=~a_1~+~(n-1)\cdot 4\\\\\\113~=\,-3~+~4n~-~4\\\\\\4n~=~113~+~3~+~4\\\\\\4n~=~120\\\\\\n~=~\dfrac{120}{4}\\\\\\\boxed{n~=~30~termos}\\\\\\\Huge{\begin{array}{c}\Delta \tt{\!\!\!\!\!\!\,\,o}\!\!\!\!\!\!\!\!\:\,\perp\end{array}}Qualquer~d\acute{u}vida,~deixe~ um~coment\acute{a}rio$