Question

How many terms of the series 1+3+9+ ...sum to 364?

• A. 5
• B. 6
• C. 4
• D. 3

Answer 1

Answer: (B)

6

The above sequence is a G.P with a common difference of 3, and first term 1.

Thus sum of G.P is

$S_n=\frac{1(3^n-1)}{3-1}$

$=\frac{3^n-1}{2}$

$S_n=364$

Hence

$\frac{3^n-1}{2}=364$

$3^n-1=728$

$3^n=729$

$3^n=3^6$

$n=6$.