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)

3

Answer 2

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