Question

Sum of all terms of a G.P. is $5$ times the sum of odd terms, The common ratio is

• A. $5$
• B. $4$
• C. $3$
• D. $2$

Answer 1

The correct option is B $4$

$\text{Given,}$

$\text{The sum of G.P of even numbers}$

$\text{terms is equal to}5\text{times the}$

$\text{sum of odd terms.}$

$\text{Let,}$

$\text{Terms in G.P is, (even terms)}$

$a,ar,a{r}^2,.........\text{with}2n\text{terms}$

$a,a{r}^2,a{r}^4........\text{(odd terms)}$

$\text{sum}=\frac{a(r^{2n}-1)}{(r-1)}$

$\text{According to question}$

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

$\Rightarrow (r+1)(r-1)=5(r-1)$

$\Rightarrow r+1=5$

$\Rightarrow r=4$

$\text{option}B=r=4$