If the coefficients of `a^(r-1),\ a^r a n d\ a^(r+1)` in the binomial expansion of `(1+a)^n` are in A.P., prove that `n^2-on(4r+1)+4r^2-2=0.`

If the coefficients of a^(r-1),\ a^r and \ a^(r+1) in the binomial expansion of (1+a)^n are in A.P., prove that n^2-n(4r+1)+4r^2-2=0.

In the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the binomial expansion of (1+y)^m are in A.P., then prove that m^2-m(4r+1)+4r^2-2=0.

In the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the binomial expansion of (1+y)^m are in A.P., then prove that m^2-m(4r+1)+4r^2-2=0.

If the coefficient of the rth, (r+1)th and (r+2)th terms in the expansion of (1+x)^(n) are in A.P., prove that n^(2) - n(4r +1) + 4r^(2) - 2=0 .

If the coefficient of r^(th) ,( r +1)^(th) " and " (r +2)^(th) terms in the expansion of (1+x)^n are in A.P then show that n^2 - (4r +1)n + 4r^2 - 2 =0

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

If the coefficient of (3r)^(th) and (r + 2)^(th) terms in the expansion of (1 + x)^(2n) are equal then n =

If for positive integers r gt 1, n gt 2 , the coefficients of the (3r) th and (r+2) th powers of x in the expansion of (1+x)^(2n) are equal, then prove that n=2r+1 .

If the coefficients of rth, (r + 1)th and (r + 2)th terms in the expansion of (1 + x)^n be in H.P. then prove that n is a root of the equation x^2 - (4r - 1) x + 4r^2 = 0.

If the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the expansion of (1+x)^(14) are in A.P., then r is/are a. 5 b. 11 c. 10 d. 9