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Coefficients of three consecutive terms (or powers) in A.P.

This type of question, asked 3 times: 4 Apr 2024, 24 Jan 2025, 23 Jan 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    4 Apr 2024

    163
    If the coefficients of x4,x5x^{4},x^{5} and x6x^{6} in the expansion of (1+x)n(1 + x)^{n} are in the arithmetic progression, then the maximum value of nn is:

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  2. Question 2

    24 Jan 2025

    66
    For some n≠10n \neq 10, let the coefficients of the 5th ,6th 5^{\text{th~}},6^{\text{th~}} and 7th 7^{\text{th~}} terms in the binomial expansion of (1+x)n+4(1 + x)^{n + 4} be in A.P. Then the largest coefficient in the expansion of (1+x)n+4(1 + x)^{n + 4} is :

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  3. Question 3

    23 Jan 2026 S1

    64
    The sum of all possible values of n∈Nn \in N, so that the coefficients of x,x2x,x^{2} and x3x^{3} in the expansion of (1+x2)2(1+x)n\left( 1 +x^{2} \right)^{2}(1 + x)^{n}, are in arithmetic progression is :

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