23 Maths -- Sequence and Series

If a, b, c be in AP, b, c, d be in GP and c, d, e be in HP, prove that a, c, e are in GP.

If a, b, c be in AP, b, c, d be in GP and c, d, e be in HP, prove that a, c, e are in GP.

1 Answers

More questions on Sequence and Series

If GM and HM between two positive numbers a and b are such that GM=5/4 HM, prove that a:b=4:1.

If x^2, b^2, y^2 are in AP, a, x, b and b, y, c both are in GP, prove that a, b, c are in AP.

The A.M., G.M. and H.M. between any two unequal positive numbers satisfy the relations (a) (G.M.)2  = (A.M.) x (G.M.)             (b) A.M. > G....

Let a and b be two unequal positive numbers. Then,

A.M. = (a+b)/2 G.M = (ab)

and, H.M. = 2ab/(a+b)
To Prove the first part, we have

(A.M.) x (G.M.) = (a+b)/2 x 2ab/(a+b)

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