Question

The fourth, seventh and tenth terms of a G.P. are $p,q,r$ respectively, then:

• A. $p^2=q^2+r^2$
• B. $q^2=pr$
• C. $p^2=qr$
• D. $pqr+pq+1=0$

Answer 1

Answer: (B)

Let $a$ be the first term and $r$ be common ratio.
Fourth term of G.P. $:p=T_4=a{r}^3\dots (i)$
Seventh term of GP. : $q=\frac{4}{T_7}=a{r}^6....(ii)$
Tenth term of G.P. : $r=T_{10}=a{r}^9\dots (iii)$
Equ. (i) $\times$ Equ. (iii):
$pr=a{r}^3\times a{r}^g$
$\Rightarrow pr=a^2{r}^{12}$
$\Rightarrow pr={\left(a{r}^6\right)}^2$
$\Rightarrow pr=q^2$