Question

What is the sum of the geometric series below?

3+1+1/3+1/9+1/27


a. 67/27
b. 121/27
c. 40/9
d. 41/9

Answer 1

answer is b. 121/27

3+1+1/3+1/9+1/27
= 3+1+9/27+3/27+1/27
= 4 13/27
= 121/27

Answer 2

Option B is correct.

Explanation:

Given Geometric series : 3 , 1 ,
`(1)/(3)\:,\:(1)/(9)\:,\:(1)/(27)`

To find: Sum of the series.

First term of the geometric series, a = 3

Common ration of the Geometric series, r =
`(second\:term)/(first\:term)=(1)/(3)`

Sum of the finite Geometric series ,
`S_n=(a(1-r^n))/(1-r)`

Sum of the given 5 term term of given series ,
`S_5=(3(1-((1)/(3))^5))/(1-(1)/(3))=(3((3^5-1)/(3^5)))/((3-1)/(3))`

=
`((3^5-1)/(3^3))/(2)=(243-1)/(2*3^3)=(121)/(27)`

Therefore, Option B is correct.