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,…………120}

(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,…………120}?
Solution:-

The given set {1, 2, 3, 4, 5, ……….., 120} has 60 even & 60 odd integers.
Now let three numbers be a, b, c which are in A.P.
then

so (a + c) is also even & this can happen by 2 ways:-