Question

If pth, qth, rth terms of a G.P. are in G.P., then p, q, r are in

• A. A.P
• B. G.P.
• C. H.P
• D. p = q = r

Answer 1

Answer: (A)

Since $T_p,T_q,T_r$ are in $G.P$.
$\therefore T_q^2=T_p.T_r$
$\therefore {\left(A{R}^{q-1}\right)}^2=A{R}^{p-1}.A{R}^{r-1}$
$\Rightarrow 2q-2=p+r-2$
$\Rightarrow 2q=p+r$
$\Rightarrow p,q,r$ are in $A.P$.