Browse Questions

If $a, b, c$ are in $AP, a, x, b$ and $b, y, c$ in $GP$, what is the progression type for $x^2,b^2,y^2$?

$\begin{array}{1 1} AP \\ GP \\ HP \\ None\;of\;the \;above \end{array}$

Explanation : a,b,c in AP 2b=a+c
a,x,b in GP $x^2=ab$
b,y,c in GP $y^2=bc$
$x^2+y^2=ab+bc=b(a+c)$
$=b\;(2b)$
$=2\;b^2$
$x^2\;,b^2\;y^2\;are\;in\;AP.$