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Question

If A1,A2 be two AM′s and G1,G2 be two GM′s between two numbers a and b, then A1+A2G1G2 is equal to

A
a+b2ab
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B
2aba+b
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C
a+bab
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D
aba+b
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Solution

The correct option is B a+bab
As per question
AP series will be a,A1,A2,b
d=ba3
A1=a+ba3=(2a+b)/3
A2=a+2(ba)3=(a+2b)/3
GP series will be a,G1,G2,b
r=(ba)1/3
G1=a(ba)1/3=b1/3a2/3
G2=a(ba)2/3=b2/3a1/3
Required ratio will be A1+A2G1G2=2a+b3+a+2b3a1/3b2/3a2/3b1/3=a+bab


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