Question

If $m^{th}$, $n^{th}$ and $p^{th}$ terms of a G.P. form three consecutive terms of a geometric progression , then $m,n,p$ are in

• A. A.P.
• B. G.P.
• C. H.P.
• D. none of these

Answer 1

Answer: (A)

A.P.

$T_m=a{r}^{m-1}$
$T_n=a{r}^{n-1}$
$T_p=a{r}^{p-1}$
$T_m,T_n,T_p$ are in G.P.
$T_n^2=T_m\times T_p$
$a^2{r}^{2n-2}=a{r}^{m-1}\times a{r}^{p-1}$
$r^{2n-2}=r^{m+p-2}$
$⟹2n-2=m+p-2$
$⟹2n=m+p$
$⟹$ $m,n,p$ are in $A.P.$