Show that $(a−b)^2,\ (a^2+b^2),\ (a+b)^2$ are in A.P.

Given: $(a−b)^2,\ (a^2+b^2),\ (a+b)^2$ 

To do: To show that $(a−b)^2,\ (a^2+b^2),\ (a+b)^2$ are in A.P.

Assume that $( a−b)^2,\ ( a^2+b^2)$ and $(a+b)^2$ are in AP.

$( a^2+b^2)−( a−b)^2=( a+b)^2−( a^2+b^2)$

$(a^2+b^2)−(a^2+b^2−2ab)=a^2+b^2+2ab−a^2−b^2$

 

$2ab=2ab$

Because, difference between two consecutive terms is the same.

Hence given terms are in A.P.