Question

Encontre o decimo termo da P. G. (-48, -24, -12,...)

Answer 1

Temos que:

 

$\text{q}=\dfrac{\text{a}_2}{\text{a}_1}=\dfrac{\text{a}_3}{\text{a}_2}=\dfrac{-24}{-48}=\dfrac{-12}{-24}=\dfrac{1}{2}$

 

Logo:

 

$\text{a}_{\text{n}}=\text{a}_1\cdot\text{q}^{\text{n}-1}$

 

$\text{a}_{10}=-48\cdot\left(\dfrac{1}{2}\right)^{10-1}$

 

$\text{a}_{10}=-48\cdot\left(\dfrac{1}{2}\right)^9$

 

$\text{a}_{10}=-48\cdot\dfrac{1}{512}$

 

$\text{a}_{10}=\dfrac{-48}{512}=\dfrac{-3}{32}$