Question

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

Answer 1

`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`