Question

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

Answer 1

$S=4^1+4^2+4^3+\cdots+4^8$
$4S=4^2+4^3+4^4+\cdots+4^9$
$\implies4S-S=3S=4^9-4^1$
$\implies S=\dfrac{4^9-4}3=87,380$