The absolute values of the coefficients of the second, third and fourth terms of the (1-x) ^ n expansion form an arithmetic sequence, and the middle term of the expansion is obtained

The absolute values of the coefficients of the second term, the third term and the fourth term are n, n (n-1) / 2 and n (n-1) (n-2) / 6, respectively. From the known results, N + n (n-1) (n-2) / 6 = n (n-1), the two ends are divided by n to get 1 + (n-1) (n-2) / 6 = n-1, n ^ 2-9n + 14 = 0, and the solution is n = 7 or n = 2 (rounding off)

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