Question

If the $4^{th}$, $7^{th}$ and ${10}^{th}$ terms of a G.P. be a, b, c respectively, then the relation between a, b, c is _______.

Answer 1

Let first term of G.P. = A and common ratio = r

We know that nth term of G.P. = $A{r}^{n-1}$

Now $t_4$ = a = $A{r}^3$, $t_7$ = b = $A{r}^6$ and $t_{10}$ = $A{r}^9$

Relation $b^2$ = ac is true because $b^2$ = $(A{r}^6{)}^2$ = $A^2{r}^{12}$ and ac = $\left(A{r}^3\right)\left(A{r}^9\right)$= $A^2{r}^{12}$