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

Answer:

Sum of the geometric sequence is 19662.

Step-by-step explanation:

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

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

In this formula a = first term

r = common ratio

n = number of terms

Given in the question

a = 6

r = (-4)

n = 7

$S_{7}=(6)\frac{[1-(-4)^{7}] }{[1-(-4)]}=6.\frac{(1+16384)}{(1+4)}=\frac{(6)(16385)}{5}= 19662$

Therefore sum of the sequence is 19662

Answer 2

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