Let n be a positive integer . If the
cofficients of rth (r +1) th and (r +2)th terms in the expansion of ` (1 + x)^(n) ` are in AP, then find the relation between n and r .

Explanation

To find the relationship between \( n \) and \( r \) given that the coefficients of the \( r \)-th, \( (r+1) \)-th, and \( (r+2) \)-th terms in the expansion of \( (1 + x)^n \) are in Arithmetic Progression (AP), we can follow these steps:

### Step 1: Identify the coefficients of the terms
The coefficients of the \( r \)-th, \( (r+1) \)-th, and \( (r+2) \)-th terms in the expansion of \( (1 + x)^n \) are given by:
- Coefficient of \( r \)-th term: \( \binom{n}{r} \)
- Coefficient of \( (r+1) \)-th term: \( \binom{n}{r+1} \)
- Coefficient of \( (r+2) \)-th term: \( \binom{n}{r+2} \)

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