Question

If the $5^{th},8^{th},{11}^{th}$ terms of a $G.P.$ are $p,q$ and $r$ respectively, then ?

• A. $p+r=2q$
• B. $q+r=2p$
• C. $n+a=2r$
• D. $pr=q^2$

Answer 1

The correct option is D $pr=q^2$

Let 'a' be the first term and 'r' be the common ratio of the G.P

According to question

$a_5=a{r}^{s-1}=a{r}^4=p$......(1)

$a_8=a{r}^{8-1}=a{r}^7=q$.......(2)

$a_{11}=a{r}^{-1}=a{r}^{10}=r$.......(3)

Divide (2) and (1)

$\Rightarrow r^3=\frac{q}{p}$......(4)

Again, divide (3) and (2)

$\Rightarrow r^3=\frac{r}{q}$.......(5)

Now, equate $\left(4\right)$ and $\left(5\right)$

$\frac{q}{p}=\frac{r}{q}$

$pr=q^2$