Question

Sabendo que a31 = 169 e a51 = 229 calcule a razão dessa PA.

Answer 1

$\mathrm{PA\ \to\ a_{31}=169\ \ \| \ \ a_{51}=229\ \ \| \ \ r=?}\\\\ \textrm{Atrav\'es do termo geral, teremos que:}\\\\ \mathrm{a_n=a_k+(n-k).r\ \to\ a_{51}=a_{31}+(51-31).r}\\\\ \mathrm{a_{51}=a_{31}+20.r\ \to\ 229=169+20r}\\\\ \mathrm{20.r=229-169\ \to\ 20.r=60\ \to\ r=\dfrac{60}{20}}\\\\ \mathbf{r=3}$