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. $320$
• B. $640$
• C. $2430$
• D. $7290$

Answer 1

Answer: (A)

$320$

Let the first three terms of GP be $\frac{a}{r},a,ar$

Given, product $=1000$

$\Rightarrow a^3=1000$

$\Rightarrow a=10$
Now, $T_3+T_4=60$

$ar+a{r}^2=60$

$\Rightarrow r^2+r-6=0$

$\Rightarrow (r+3)(r-2)=0$

$\Rightarrow r=2$ ($r=-3$ is not possible as it would make first term $\frac{a}{r}$ negative)
Now, $T_7=a{r}^5$

$\Rightarrow T_7=10(2{)}^5=320$