Question

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

Answer 1

$2b=a+c,b^2=ac$
Eliminating $b$, we get $(a+c{)}^2=4ac$
$\therefore (a-c{)}^2=0$ $\therefore a=c$ and hence $b=a$