If the coefficients of `a^(r-1),a^r`and `a^(r+1)`in the expansion of `(1+a)^n`are in arithmetic progression, prove that `n^2-n(4r+1)+4r^2-2=0`.

Explanation

To solve the problem, we need to find the coefficients of \( a^{r-1} \), \( a^r \), and \( a^{r+1} \) in the expansion of \( (1 + a)^n \) and show that they are in arithmetic progression.

### Step 1: Identify the coefficients
The coefficients of \( a^{r-1} \), \( a^r \), and \( a^{r+1} \) in the expansion of \( (1 + a)^n \) can be found using the binomial theorem, which states that:
\[ (1 + a)^n = \sum_{k=0}^{n} \binom{n}{k} a^k \]
Thus, the coefficients are:
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