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

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

In the coefficients of rth,(r+1) th,and (r+2) 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.