Question

The sum of first three terms of an increasing G.P. is $13$ and their product is $27$. The sum of the first $5$ terms is:-

• A. $363$
• B. $\frac{40}{3}$
• C. $243$
• D. $121$

Answer 1

The correct option is A $363$

Let the G.P be $\frac{a}{r},a,ar$.

So,

$\frac{a}{r}+a+ar=13$

And

$\frac{a}{r}\times a\times ar=27$

$a^3=27$

$a=3$

Therefore,

$\frac{3}{r}+3+3r=13$

$3+3r+3r^2=13r$

$3r^2-10r+3=0$

$3r^2-9r-r+3=0$

$3r(r-3)-1(r-3)=0$

$(3r-1)(r-3)=0$

$r=\frac{1}{3},3$

So, $r=3$

So, the G.P is $1,3,9$.

Now, the sum of first five terms

$=\frac{3(3^5-1)}{3-1}$

$=\frac{3(243-1)}{2}$

$=\frac{3\left(242\right)}{2}$

$=3\left(121\right)=363$

Hence, this is the answer.