Question

In a GP of even number of terms, the sum of all terms is 5 times the sum of the odd terms. The common ratio of the GP is

• A. $\frac{-4}{5}$
• B. $\frac{1}{5}$
• C. $4$
• D. none of these

Answer 1

Answer: (C)

$4$

Let G.P be $a,ar,.......a{n}^n,....................,a{r}^{2n}$
So sum of all termss $=S_{all}=\frac{a(1-r^{2n})}{1-r}$
and sum of odd terms $=S_{odd}=\frac{a(1-(r^2{)}^n)}{1-r^2}=\frac{a(1-r^{2n})}{1-r^2}$
Now given $S_{all}=5\cdot S_{odd}$
$\Rightarrow (1-r^2)=5(1-r)$
$\Rightarrow r^2-5r+4=0\Rightarrow r=1or4$ (but $r\ne 1)$
Hence common ratio of the required G.P is 4.