Question

The sum of the $3^{rd}$ and the $4^{th}$ terms of a $G.P.$ is $60$ and the product of its first three terms is $1000$. If the first term of this $G.P.$ is positive, then its $7^{th}$ term is :

• A. 7290
• B. 320
• C. 640
• D. 2430

Answer 1

Answer: (B)

$a r^{2}+a r^{3}=60 ; a \cdot$ ar $\cdot a r^{2}=1000, a >0$
$\Rightarrow a r^{2}(1+r)=60 ; a^{3} r^{2}=1000, a>0$
$\Rightarrow a r=10$
$\Rightarrow \frac{a r^{2}(1+r)}{a r}=\frac{60}{10}$
$\Rightarrow r(r+1)=6$
$\Rightarrow r=2$
$\Rightarrow a=5$
$\Rightarrow T_{7}=a r^{6}=(5)(2)^{6}=320$