Question

If the $p^{th}$, $q^{th}$ and $r^{th}$ terms of an AP are in GP then the common ratio of GP is

• A. $\frac{p+q}{r+q}$
• B. $\frac{r-q}{q-p}$
• C. $\frac{p-r}{p-q}$
• D. None of these

Answer 1

The correct option is B $\frac{r-q}{q-p}$

Given

$\frac{a+(q-1)d}{a+(p-1)d}=\frac{a+(r-1)d}{a+(q-1)d}$

$\Rightarrow \frac{(q-p)d}{a+(p-1)d}=\frac{(r-q)d}{a+(q-1)d}$

$\Rightarrow \frac{a+(q-1)d}{a+(p-1)d}=\frac{r-q}{q-p}$

$\therefore$ Option B is correct.