If the coefficients of the  (r + 2)th and   rth, (r + 1)th terms in the binomial expansion of (1 + y)m are in , then  A.P.m and r satisfy the equation

Coefficient of the r th  term is  mCr−1According to the given condition nmCr−1+mCr+1=2 mCr⇒     mCr−1 mCr+ mCr+1 mCr=2⇒rm+1−r+m−rr+1=2⇒    r2+r+(m−r)(m+1−r)=2(m+1−r)(r+1)⇒    r2+r+m2+(1−2r)m−r(1−r)=    ⇒2m(r+1)+21−r2⇒     m2−m(4r+1)+4r2−2=0.