An important and exam oriented question from arithmetic progression chapter as it was already asked in previous year paper of 2009 in which we are to find for what value of x the numbers x+2, 2x, 2x+3 are three consecutive terms of an A.P.
RS Aggarwal, Class 10, chapter 5B, question no 4.
Assume that (a−b)2,(a2+b2) and (a+b)2 are in AP.
So, difference between two consecutive terms will be same.
(a2+b2)−(a−b)2=(a+b)2−(a2+b2)
(a2+b2)−(a2+b2−2ab)=a2+b2+2ab−a2−b2
2ab=2ab
Which is true.
Hence given terms are in AP.