If n arithmetic means are inserted between two sets of numbers a, 2b and 2a, b, where a,bϵR. Suppose that mth arithmetic mean between these two sets of numbers is same, then the ratio a:b equals
A
n - m + 1:m
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B
n - m + 1:n
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C
m:n - m + 1
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D
n:n - m + 1
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Solution
The correct option is C m:n - m + 1 Let A1,A2.....An be airthmetric means between a and 2b , then Am=a+m(2b−an+1) Again, let B1,B2.....Bn be arithmetic means Between 2a and b then Bm=2a+m(b−2an+1) Now, Am=Bm⇒a+m(2b−an+1)=2a+ m(b−2an+1)⇒m(b+an+1)=a⇒ab=mn−m+1