Find the sum of the first n terms of the geometric series…show work please?

1 + 4 + 16 + 64

n=14

Top 1 Answers

A few days ago

MsMath

Favorite Answer

Note that

1 = 4^0

4 = 4^1

16 = 4^2

64 = 4^3

This is the sum of (4^k), from k = 0 to 14

The formula for the sum of the first n terms of

ar^k, when k starts at 0 is

a(1 – r^(n+1)) / (1-r)

a = 1, r = 4, and n = 14

Plug those into the formula.

1(1 – 4^(14+1)) / (1-4)

= (1 – 4^15) / (-3)

= (1 – 1,073,741,824) / (-3)

= -1,073,741,823 / (-3)

= 357,913,941

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