Binomial TheoremHard

Question

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

Options

A.m2 - m(4r - 1) + 4r2 - 2 = 0
B.m2 - m(4r + 1) + 4r2 + 2 = 0
C.m2 - m(4r + 1) + 4r2 - 2 = 0
D.m2 - m(4r - 1) + 4r2 + 2 = 0

Solution

Given mCr-1′ + mCr′ + mCr+1 are in A.P.
2mCr = mCr-1 + mCr+1
⇒   2 =

⇒   m2 - m (4r + 1) + 4r2 - 2 = 0.

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