Question

.1. Find the sum, S., of the geometric series given a = 4, r = 4, and n = 6. Remember to use the formulas,OS.--16384O S. - 5460OS, - 1365O S. - 1024

Answer 1

A geometric series is the sum of the terms in a geometric sequence. The formula for the sum of the first n terms of a geometric sequence is represented as:

$S_n=\frac{a(1-r^n)}{1-r}$

Where:

a = 4

r = 4

n = 6

Substitute the values:

$S=\frac{4(1-4^6)}{1-4}$

Simplify:

$S=\frac{4(1-4096)}{1-4}=\frac{4(-4095)}{-3}=\frac{-16380}{-3}=5460$

Answer: 5460