Let r=2 ∴2nd, 3rd and 4th terms are in AP. 2nd term =T2=mC1⋅y Coefficient of T2=mC1 3rd term =T3=mC2⋅y2 Coefficient of T3=mC2 4th term =T4=mC3⋅y3 Coefficient of T2=mC3 ∴2.mC2=mC1+mC3 ⇒2.
m(m−1)
1.2
=
m
1
+
m(m−1)(m−2)
1.2.3
⇒6m2−6m=6m+m(m2−3m+2) ⇒6m2−6m=6m+m3−3m2+2m ⇒6m−6=6+m2−3m+2 ⇒m2−9m+14=0 Now put r=2 at each option and find answer. In option C, m2−m(4r+1)+4r2−2=0 putting r=2 we get m2−9m+14=0. So Option C is correct.