The coefficients of the second, third and fourth terms of the expansion of (√ x + 1 / x) ^ n are known to form an arithmetic sequence, and N is obtained

The coefficients of the second, third and fourth terms of the expansion of (√ x + 1 / x) ^ n are known to form an arithmetic sequence, and N is obtained

C (n) (m) refers to permutation
The 234 coefficients are n c (2) (n) C (3) (n)
So 2C (2) (n) = n + C (3) (n)
2*n!/((n-2)!*2!)=n+n!/((n-3)!*3!)
n(n-1)=n+n(n-1)(n-2)/6
So n = 0 or 2 or 7
Since there is a fourth term in the decomposition, 0,2 is rounded off
n=7