Question

If $a,b,c$ are in $A.P.a,mb,c$ are in $G.P.$ then $a,m^{2}b,c$ are in

Answer 1

$a,b,c$ are in $A.P$ $⟹2b=a+c$

$a.mb,c$ are in $G.P$ $⟹m^2{b}^2=ac$

$\frac{1}{a}+\frac{1}{c}=\frac{a+c}{ac}=\frac{2b}{m^2{b}^2}=\frac{2}{m^{2}b}$

$⟹a,m^{2}b,c$ are in $H.P$