If an even number of A.M.s are inserted between two numbers whose sum is 136, such that their sum exceeds their numbers by unity, then the number of means is
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Solution
Let a and b be two numbers and 2n A.M.s are inserted between a and b then a,A1,A2,....,A2n,b be in A.P.
Given a+b=136 A1+A2+....+A2n=2n+1 ⇒2n2×136=2n+1 ⇒13n=12n+6⇒n=6
Hence number of means =2n=12