Question

The product of the third and eighth term of a geometric progression is 243. If the term is 3 , seventh term of the GP.find the s

Answer 1

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,

$a{r}^3=3$

$a{r}^2\times a{r}^7=243$

On solving the given equations, we get $a=\frac{1}{9}$ and $r=3.$

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

Hence, this is the answer.