Question

determine a P.A cujo o sétimo termo vale 1 e o décimo termo vale 16

Answer 1

$a_n=a_1+(n-1)r$

$a_7=a_1+6r~~\Rightarrow~~a_1+6r=1~~(i)$

$a_{10}=a_1+9r~~\Rightarrow~~a_1+9r=16~~(ii)$.

Subtraindo $(ii)-(i)$:

$(a_1+9r)-(a_1+6r)=16-1~~\Rightarrow~~3r=15~~\Rightarrow~~\boxed{r=5}$

$a_1+6r=1~~\Rightarrow~~a_1+30=1~~\Rightarrow~~\boxed{a_1=-29}$.

A PA em questão é $(-29,-24,-19,-14,-9,-4,1,6,11,16)$