Question

quantos termos tem a P.G.(8,32,....,2³¹)?

Answer 1

Facin mano,

substitua tudo na fórmula do termo geral..

$a_1=8\\ a_n=2^{31}\\ q=(a_2)/(a_1)=32/8=4\\n=?$

assim..

$a_n=a_1\cdot q^{n-1}\\ 2^{31}=8\cdot4^{n-1}\\ 2^3\cdot4^{n-1}=2^{31}\\ 2^3\cdot4^n\cdot4^{-1}=2^{31}\\ 2^3\cdot(2^2)^n\cdot(2^2)^{-1}=2^{31}\\ 2^3\cdot2^{2n}\cdot2^{-2}=2^{31}\\ 2^{2n}\cdot2^{3-2}=2^{31}\\ 2^{2n}\cdot2^1=2^{31}\\\\ 2^{2n}= \dfrac{2^{31}}{2^1}\\\\ \not2^{2n}=\not2^{30}\\\\ 2n=30\\\\ n=30/2\\\\ \Large\boxed{n=15~termos}$

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