In the expansion of 1-2x) n, if the binomial coefficients of the second, third and fourth terms form an arithmetic sequence, then the fifth term is

In the expansion of 1-2x) n, if the binomial coefficients of the second, third and fourth terms form an arithmetic sequence, then the fifth term is

The binomial coefficient of the second term is NC1, the binomial coefficient of the third term is NC2, and the binomial coefficient of the fourth term is NC3. Because it is an arithmetic sequence, NC1 + NC3 = 2 * nc2n + n * (n-1) * (n-2) / 6 = 2 * n * (n-1) / 21 + (n ^ 2-3n + 2) / 6 = n-16 + n ^ 2-3n + 2 = 6n-6n ^ 2-9n + 14 = 0 (n-2) * (N-7) = 0, so n = 2 (rounding)