Question

If the 4th, 7th and 10th terms of aq 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 $b^2$ = $(A{r}^6{)}^2$ = $A^2{r}^{1}2$ 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. are always in G.P., therefore a, b, c will be in G.P. i.e. $b^2$ = ac.