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Question

Find the relation between x and y in order that the rth mean between x and 2y may be the same as the rth mean between 2x and y, n means being inserted in each case.

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Solution

When n means are inserted between a and b, common difference d=ban+1 and rth mean =a+rd

Therefore x+r×(2yxn+1)=2x+r×(y2xn+1)

(n+1)x+2ryrx=2(n+1)x+ry2rxy=(nr+1r)x

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