Question

Em uma P.A crescente o 3 termo foi-80 e o 7 termo e -5 qual o 1 termo

Answer 1

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

$a_m~=~a_n+(n-1)\,.\,r\\\\\\a_7~=~a_3+(7-3)\,.\,r\\\\\\-5~=\,-80+4r\\\\\\4r~=\,-5+80\\\\\\\boxed{r~=~\frac{75}{4}}$

Agora, utilizando novamente a equação do termo geral, podemos determinar o valor de a₁:

$a_1~=~a_7+(1-7)\,.\,r\\\\\\a_1~=~-5-6\,.\,\frac{75}{4}\\\\\\a_1~=~-5-\frac{225}{2}\\\\\\a_1~=~\frac{2\,.\,(-5)+1\,.\,(-225)}{2}\\\\\\a_1~=~\frac{-10-225}{2}\\\\\\\boxed{a_1~=\,-\frac{235}{2}}$