Question

The product of $3^{rd}$ and $8^{th}$ terms of a G.P. is 243. If its $4^{th}$ term is 3, find its $7^{th}$ term.

Answer 1

7th term will be 81.

Suppose a is the first term and r the ratio.

$a,ar,a{r}^2,a{r}^3,a{r}^4,a{r}^5,a{r}^6,a{r}^7$are the 8 terms.

Given,

$a{r}^3$=3,
$\left(a{r}^2\right)\times \left(a{r}^7\right)$=243

Solving the given equations we get a = 1/9 and r = 3.

So the 7th term is $a{r}^6=\frac{1}{9}\times 3^6$ = 81.