Question:medium
The sum of all possible values of \( n \in \mathbb{N} \), so that the coefficients of \(x, x^2\) and \(x^3\) in the expansion of \((1+x^2)^2(1+x)^n\) are in arithmetic progression is :
The sum of all possible values of \( n \in \mathbb{N} \), so that the coefficients of \(x, x^2\) and \(x^3\) in the expansion of \((1+x^2)^2(1+x)^n\) are in arithmetic progression is :
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For small \(n\), you can quickly test values. For \(n=3\), coeffs are \(3, 5, 7\), which are clearly in AP with a common difference of 2.
Updated On: Mar 16, 2026
- 9
- 3
- 7
- 12
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The Correct Option is B
Solution and Explanation
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