Question

What is the sum of a 7-term geometric series if the first term is 6, the last term is 24,576, and the common ratio is −4?

Answer 1

The shortest way is to use the sum formula for GP


S =a(1-rⁿ) /(1-r)

a=6

r=(-4)

n=7 (seventh term) ===> S=6(1-(- 4)⁷)/[1- -4)] =19,662

Answer 2

Sum of the geometric sequence is 19662.

Explanation:

Sum of the terms in a geometric series is represented by the formula

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

In this formula a = first term

r = common ratio

n = number of terms

Given in the question

a = 6

r = (-4)

n = 7

`S_(7)=(6)([1-(-4)^(7)] )/([1-(-4)])=6.((1+16384))/((1+4))=((6)(16385))/(5)= 19662`

Therefore sum of the sequence is 19662