Q19 of 110 Page 41

If a2, b2, c2are in A.P. then show that are also in A.P.

Given, a2, b2 and c2 are in A.P.


We know that when t1, t2, t3 … are in A.P., t3 – t2 = t2 – t1


⇒ b2 – a2 = c2 – b2


We know that a2 – b2 = (a – b) (a + b)


⇒ (b – a) (b + a) = (c – b) (c + b)


⇒ =


Dividing by (c + a) on both sides,


⇒ =


⇒ =


⇒


Hence, , and are in A.P.


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