Q. 19

# 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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