1.

If a b c are in ap prove that b+c c+a a+b are also in ap

Answer»

A, B and C are in AP

Let B = A + d

C = A + 2d , d = common difference

Let 2A + d = X

So A + B = A + A + d = 2A + d = X

A + C = A + A + 2d = 2A + 2d = X +  d

B + C = A + d + A + 2d = 2A + 3d = X + 2d

Now see that X, X+d and X+2d are in AP.

That is A+B, A+C and B+C are in AP

HOPE THIS HELPS YOU........


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