Question

If the second and fifth terms of a $GP$ are $24$ and $3$ respectively, then the sum of first six terms is

• A. $181$
• B. $\frac{181}{2}$
• C. $189$
• D. $\frac{189}{2}$
• E. $191$

Answer 1

The correct option is D $\frac{189}{2}$

Let $a$ be first term and $r$ be common ratio.

$t_2=ar=24$ and $t_5=a{r}^4=3$

$\frac{t_5}{t_2}=\frac{a{r}^4}{ar}=\frac{3}{24}$

$\Rightarrow r^3=\frac{1}{8}$

$\Rightarrow r=\frac{1}{2}$

and $a\times \frac{1}{2}=24\Rightarrow a=48$

Now, $S_6=\frac{a(1-r^6)}{1-r}=\frac{48(1-\frac{1}{64})}{1-\frac{1}{2}}=\frac{48\times 63\times 2}{64}=\frac{189}{2}$

Hence, D is the correct option.