Question

The coefficient of y^n,y^n+1, y^n+2 in the binomial expansion of (1+y)^14 are in AP. Find the possible values of n.

Answer 1

the coefficients are C(14,n+1), C(14,n+2), C(14,n+3)

Due to the symmetry of the coefficients, we only have to consider
n=0,1,2,3,4,5
These sets of coefficients are
1,14,91
14,91,364
91,364,1001
364,1001,2002
1001,2002,3003
2002,3003,3432
So the smallest value of n=4 = 7-3
the other (largest) value would be n+2 = 7+3 = 10, so n=8