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=(a(1-r^n))/(1-r)`

Where:

a = 4

r = 4

n = 6

Substitute the values:

`S=(4(1-4^6))/(1-4)`

Simplify:

`S=(4(1-4096))/(1-4)=(4(-4095))/(-3)=(-16380)/(-3)=5460`

Answer: 5460