Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

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
$ac=\left(A{r}^3\right)\left(A{r}^9\right)=A^2{r}^{12}$

Aliter: As we know, if p,q, r in A.P. then $p^{th},q^{th},r^{th}$ terms of a G.P. will satisfy the condition $b^2=ac$.