Question

If the fourth, seventh and tenth terms of a $G.P$ are $p,q,r$ respectively then $q^2=pr$

• A. True
• B. False

Answer 1

The correct option is A True

We have,

$a_4=p$

$a{r}^3=p$ $............\left(1\right)$

Since,

$a_7=q$

$a{r}^6=q$ $............\left(2\right)$

On squaring both sides, we get

$a^2{r}^{12}=q^2$ $..........\left(3\right)$

Since,

$a_{10}=r$

$a{r}^9=r$ $.............\left(3\right)$

From equations (1) and (4),

$a{r}^3\times a{r}^9=pq$

$a^2{r}^{12}=pq$

From (3), we get

$q^2=pq$

Hence, this is the answer.