What is the sum of the geometric sequence four, 16, 64,... If there are eight terms A)21,845 B) 43,690 C)65,535 D)87,380

asked Dec 21, 2019 61.8k views

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What is the sum of the geometric sequence four, 16, 64,... If there are eight terms

A)21,845
B) 43,690
C)65,535
D)87,380

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4 votes

$S=4^1+4^2+4^3+\cdots+4^8$

$4S=4^2+4^3+4^4+\cdots+4^9$

$\implies4S-S=3S=4^9-4^1$

$\implies S=\frac{4^9-4}3=87,380$

Willj answered Dec 28, 2019

by Willj

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