Question

if $a,b,c$ are in $A.P$ as well in $G.P$., prove that $a=b=c$.

Answer 1

Since a, b, c are in A.P and G.P

Let a, b, c$=\{a-d,a,a+d\}$

$\therefore$ By condition of G.P

$\therefore a^2=a^2-d^2$

$($In G.P, $b^2=ac)$

$\therefore d^2=0$

$\therefore d=0$

$\therefore a=b=c$.