Question
The sum of two numbers is . An even number of arithmetic means are being inserted between them and their sum exceeds their number by 1. Find the number of means inserted.
Solution
Let a and b be two numbers such that
...(i)
Let be 2n (even) A.M.'s between a and b.
∴ (By using example 4)
=
Also,
∴ or 12n + 6 = 13n or n = 6
Hence, 12 A.M.'s are inserted.