Question

Fourth term of a G.P is 3 and the product of the $3^{\text{rd}}$ and $8^{\text{th}}$ term is 243. Find its $7^{\text{th}}$ term.

• A. 243
• B. 83
• C. 27
• D. 81

Answer 1

The correct option is D

81

Let the first term and the common ratio of the GP be $a$ and $r$ respectively.

By question, $a_4=a{r}^3=3.$
$\Rightarrow a=\frac{3}{r^3}...\left(1\right)$

Also, given that the product of the $3^{\text{rd}}$ and $8^{\text{th}}$ term is 243.
i.e., $a_3\times a_8=243$
$\Rightarrow a{r}^2\times a{r}^7=243$
$\Rightarrow a^2{r}^9=243...\left(2\right)$

Substituting (1) in (2), we get

$\frac{9}{r^6}\times r^9=243.$

$\Rightarrow r^3=27\Rightarrow r=3$

$\therefore a=\frac{3}{r^3}=\frac{3}{3^3}=\frac{1}{9}$

$\therefore a_7=a{r}^6=\frac{1}{9}\times 3^6=81$

Thus, the $7^{\text{th}}$ term of the GP is 81.