Question

In a geometric progression, if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49, and the sum of the first and the third term is 35. Then the first term of this geometric progression is :

• A. $21$
• B. $7$
• C. $42$
• D. $28$

Answer 1

The correct option is D $28$

Let us consider the 5 terms as $\frac{a}{r^2},\frac{a}{r},a,ar,a{r}^2$

$S_1=a[\frac{1}{r}+\frac{1}{r}+1+r+r^2]$

$S_2=\frac{1}{a}[r^2+r+1+\frac{1}{r}+\frac{1}{r^2}]$

$\therefore \frac{S_1}{S_2}=a^2=49\Rightarrow a=7$

$\frac{a}{r^2}+a=35\Rightarrow r=\frac{1}{2}$

$\therefore 1^{st}term=\frac{a}{r^2}=28$