Question

How many terms of the series 1, 4, 16,..... must be taken to have their sum equal to 341 ?

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

The correct option is C

5

Given GP is 1, 4, 16...., where $a=1$ and $r=4.$

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

i.e., $341=\frac{1(4^n-1)}{3}$

$\Rightarrow 1023=4^n-1$

$\Rightarrow 4^n=1024$

$\Rightarrow 4^n=4^5$

$\Rightarrow n=5$