Question

A series in G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying odd places, then the common ratio will be equal to

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

The correct option is

A

4

Let there be 2n terms in the given G.P. with first term a and the common ratio r.

Then $S_n=a\frac{r^{2n}-1}{r-1}$

In this case the first term which is at odd place will remain $a$ but the common ratio will become $r^2$ because the next term of the sequence will be at third position i.e. $a{r}^2$

So, now according to the question

$S_{2n}=5S_n$

Then, a $\frac{r^{2n}-1}{(r-1)}$ = 5a $\frac{(r^{2n}-1)}{(r^2-1)}$

$\Rightarrow \frac{1}{r-1}=\frac{5}{r^2-1}\Rightarrow \frac{r^2-1}{r-1}=5\Rightarrow r+1=5\Rightarrow r=4$