Question

If the $2^{nd}$ and $5^{th}$ terms of a G.P. are 24 and 3 respectively, then the sum of first six terms is _______​.

• A. $\frac{189}{2}$
• B. $\frac{189}{5}$
• C. $\frac{179}{2}$
• D. $\frac{2}{189}$

Answer 1

The correct option is A

$\frac{189}{2}$

$a,ar,a{r}^2,a{r}^4,...........G.P$

$ar=24,a{r}^4=3\Rightarrow r=\frac{1}{2},a=48$

$\therefore a+ar+a{r}^2+a{r}^3+a{r}^4+a{r}^5=a\left(\frac{1-r^n}{1-r}\right)$

$=\frac{189}{2}$