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

The coefficient of f(r+1)th  term in the expansion of (1+x)14 is  14CrIt is given that 14Cr−1,14Cr,14Cr+1 are in A.P.⇒ 214Cr=14Cr−1+14Cr+1⇒ 2= 14Cr−1 14Cr+ 14Cr+1 14Cr⇒ 2=r15−r+14−rr+1⇒ 2(15−r)(r+1)=r2+r+210−29r+r2⇒ 4r2−56r+180=0⇒ r2−14r+45=0⇒r=5,9.