If some three consecutive terms in the binomial expansion of (x+1)^n are in the ratio 2:15:70, then the average of these three coefficients is:

Let the terms be nC(r-1), nCr, nC(r+1) ⇒ nC(r-1) : nCr : nC(r+1) = 2 : 15 : 70

nC(r-1)/nCr = 2/15
[n!/(r-1)!(n-r+1)!] / [n!/r!(n-r)!] = 2/15
r/(n-r+1) = 2/15 ⇒ 15r = 2n - 2r + 2
17r = 2n + 2

nCr/nC(r+1) = 15/70
[n!/r!(n-r)!] / [n!/(r+1)!(n-r-1)!] = 3/14
(r+1)/(n-r) = 3/14
14r + 14 = 3n - 3r
17r = 3n - 14

Solving the two equations:
17r = 2n + 2
17r = 3n - 14
2n + 2 = 3n - 14
n = 16
17r = 2(16) + 2 = 34
r = 2

Therefore, the terms are 16C1, 16C2, 16C3
(16C1 + 16C2 + 16C3)/3 = (16 + 120 + 560)/3 = 700/3 = 696/3 = 232