The number of ways in which three numbers in A.P. can be selected from 1,2,3,...n is

1. A

2. B

3. C

4. D

If a,b,c are in A.P then a+c = 2b

  a,c both are odd or both are even

case (i) if n is even

let

No. of ways mC2+mC2=2m(m−1)2
=nn−24
Case (ii)

No.of ways  =n−124

Number of ways in which three numbers in A.P. can be selected from 1,2,3, ……, n is

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