Question

The sum of first 10 terms of a G.P. is equal to 244 times the sum of first five terms. Then the common ratio is

• A. 7
• B. 3
• C. 4
• D. 5

Answer 1

Answer: (B)

$S_{10}=244$
$S_5\Rightarrow \frac{a\left(1-r^{10}\right)}{1-r}=244a\frac{\left(1-r^5\right)}{1-r}$
$\Rightarrow 1-r^{10}=244\left(1-r^5\right)$
$\Rightarrow \left(1-r^5\right)\left(1+r^5\right)=244\left(1-r^5\right)$
$\Rightarrow 1+r^5=244$
$\Rightarrow r^5=243={\left(3\right)}^5$
$\Rightarrow r=3$