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 $\cdot a{r}^2=1000,a>0$
$\Rightarrow a{r}^2(1+r)=60;a^3{r}^2=1000,a>0$
$\Rightarrow ar=10$
$\Rightarrow \frac{a{r}^2(1+r)}{ar}=\frac{60}{10}$
$\Rightarrow r(r+1)=6$
$\Rightarrow r=2$
$\Rightarrow a=5$
$\Rightarrow T_7=a{r}^6=(5)(2{)}^6=320$