Question

A $GP$ consists an even number of terms. If the sum of all the terms is $5$ times the sum of the terms occupying odd places, then common ratio be equal to

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is C $4$

Assume $4$ terms in GP as

$\frac{a}{r},a,ar,a{r}^2$

$\frac{a}{r}+a+ar+a{r}^2=5(\frac{a}{r}+ar)$

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

$r^2+1+r+\frac{1}{r}-\frac{5}{r}-5r=0$

$r^3+r+r^2+1-5-5r^2=0$

$r^3-4r^2+r-4=0$

Substitute $r=4$ from options, which satisfy the above equation.