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(Q). What is the number of ways in which three numbers in A.P. can be selected from the given set {1, 2, 3, 4, 5, ……….. , 121}?
Solution:-

The given set { 1, 2, 3, 4, 5, ………..121} has \frac{{121 + 1}}{2} = 61 odd & \frac{{121 - 1}}{2} = 60 even integers.
now let three numbers from this set which are in A.P. be a, b, c

∴ 2b = a + cevenSo (a + c) is also even & this can happen by ways: -either both of a & c is odd OR both of a & c is even∴ Number of ways = Answer