Question

What is the sum of the geometric series below?

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

Answer:

Option B is correct.

Step-by-step explanation:

Given Geometric series : 3 , 1 , $\frac{1}{3}\:,\:\frac{1}{9}\:,\:\frac{1}{27}$

To find: Sum of the series.

First term of the geometric series, a = 3

Common ration of the Geometric series, r = $\frac{second\:term}{first\:term}=\frac{1}{3}$

Sum of the finite Geometric series , $S_n=\frac{a(1-r^n)}{1-r}$

Sum of the given 5 term term of given series , $S_5=\frac{3(1-(\frac{1}{3})^5)}{1-\frac{1}{3}}=\frac{3(\frac{3^5-1}{3^5})}{\frac{3-1}{3}}$

=  $\frac{\frac{3^5-1}{3^3}}{2}=\frac{243-1}{2\times3^3}=\frac{121}{27}$

Therefore, Option B is correct.