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.`

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)-on(4r+1)+4r^(2)-2=0

If the coefficients of a^(r-1), a^r and a^(r+1) in the expansion of (1+a)^n are in arithmetic progression, prove'that n^2-n(4 r+1)+4 r^2-2=0

If the coefficients of a^(r-1), a^(r ), a^(r+1) in the binomial expansion of (1 + a)^(n) are in Arithmetic Progression, prove that: n^(2) -n(4r+1) + 4r^(2) -2=0

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

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

If the coefficients of a^r-1 , a^r and a^r+1 in the expansion of (1+a)^n are in arithmetic progression, 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.