It is known that the binomial coefficients of the second term, the third term and the fourth term in the expansion of (2 ＋ x) ∧ n are arithmetic sequence! Given that the binomial coefficients of the second, third and fourth terms in the expansion of (2 ＋ x) ∧ n are equal difference sequence! 1, find the value of N 2, and find the middle term of the expansion

It is known that the binomial coefficients of the second term, the third term and the fourth term in the expansion of (2 ＋ x) ∧ n are arithmetic sequence! Given that the binomial coefficients of the second, third and fourth terms in the expansion of (2 ＋ x) ∧ n are equal difference sequence! 1, find the value of N 2, and find the middle term of the expansion

The second term 2 ^ (n-1) * √ x * n -------- > the binomial coefficient is n
The third term 2 ^ (n-2) * (√ x) ^ 2 * [n * (n-1) / 2] ---- > the binomial coefficient is n * (n-1) / 2
The fourth term 2 ^ (n-3) * (√ x) ^ 3 * [n * (n-1) * (n-2) / 6] ---- > the binomial coefficient is n * (n-1) * (n-2) / 6
According to the arithmetic sequence, 2 * [n * (n-1) / 2] = n + n * (n-1) * (n-2) / 6
n*(n-1)=n+n*(n-1)*(n-2)/6
n*(n-2)=n*(n-1)*(n-2)/6
It can be seen from the question that n > 4, so n = 7
The middle terms of the expansion are 4 and 5
Item 4 2 ^ (n-3) * (√ x) ^ 3 * [n * (n-1) * (n-2) / 6
Item 5 2 ^ (n-4) * (√ x) ^ 4 * [n * (n-1) * (n-2) * (n-3) / 24]
Substituting n = 7 into computable