Question

If the $2^{nd}$ and $5^{th}$ terms of G.P. are $24$ and $3$ respectively, then the sum of $1^{st}$ 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 $\frac{189}{2}$

Let the fist term of the G.P be $a$ and common ratio $r$

So second term $=ar=24$, given

and 5th term $=a{r}^4=3$, given

Now divide both the terms, $r^3=\frac{1}{8}={\left(\frac{1}{2}\right)}^3$

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

So $a=48$

Thus sum of first six terms $=\frac{a(1-r^6)}{1-r}=\frac{48(1-\frac{1}{64})}{1-\frac{1}{2}}=\frac{48\cdot \frac{63}{64}}{\frac{1}{2}}=\frac{189}{2}$