If the coefficient of 2nd, 3rd and 4th terms in the expansion of `(1+x)^(2n)` are in A.P. , show that `2n^2-9n+7=0.`

Explanation

To solve the problem, we need to show that if the coefficients of the 2nd, 3rd, and 4th terms in the expansion of \((1+x)^{2n}\) are in Arithmetic Progression (A.P.), then it leads to the equation \(2n^2 - 9n + 7 = 0\).

### Step-by-Step Solution:

1. **Identify the Coefficients**:
The coefficients of the terms in the binomial expansion of \((1+x)^{2n}\) are given by the binomial coefficients:
- Coefficient of the 2nd term: \(C(2n, 1) = \binom{2n}{1} = 2n\)
- Coefficient of the 3rd term: \(C(2n, 2) = \binom{2n}{2} = \frac{2n(2n-1)}{2} = n(2n-1)\)
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