If the coefficients of rth, (r + 1)th and (r + 2)th terms in the expansion of (1+x)14 are in A.P., then r is/are

coefficients of rth, (r + 1)th and (r + 2)th 14Cr−1,14Cr, and 14Cr+1If these coefficients are in A.P., then2 14Cr=14Cr−1+14Cr+1or  2(14)!r!(14−r)!=(14)!(r−1)!(15−r)!+(14)!(r+1)!(13−r)or  2(14)!r!(14−r)!=(14)!(15−r)!or  2(15−r)(r+1)=2r2−28r+210or  r2−14r+45=0 or (r−5)(r−9)=0or  r=5,9