Question

If $a,b,c$ are in $A.P$, then show that $a^2,b^2,c^2$ are also in $G.P$

Answer 1

a,b,c are in A.P

$\therefore a=b-d,b,c=b+d$

$\therefore$ Now $a^2=b^2+d^2-2bd$

$b^2=b^2$

$c^2=b^2+d^2+2bd$

$\therefore \frac{b^2}{a^2}=\frac{b^2}{b^2+d^2-2bd}$

$\therefore \frac{c^2}{b^2}=\frac{b^2{d}^2+2bd}{b^2}$

$\therefore$ From (1) & (2) , $a^2,b^2,c^2$ are in A.P.