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Question

If A1, A2 be two AM's and G1, G2 be two GM's between a and b, then find the value of A1+A2G1 G2.

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Solution

It is given that A1 and A2 are the A.M.s between a and b.Thus, a , A1, A2 and b are in A.P. with common difference d.Here, d = b-a3 A1 = a + b-a3 = 2a+b3and A2 = a + 2b-a3=a+2b3It is also given that G1 and G2 are the G.M.s between a and b.Thus, a , G1, G2 and b are in G.P. with common ratio r.Here, r = ba13 G1 = aba13 = b13 a13 and G2 = aba13 2= b13 a13 A1 + A2G1 G2 = 2a+b3+a+2b3 b13 a13 × b13 a13 = a+bab

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