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

in If the coefficient of x^(r) and x^(r+1) are equal in the expansion of (1+x)^(2n+1), then find the value of r.

If the coefficient of x^(r)andx^(r+1) are equal in the expansion of (1+x)^(2n+1) , then find the value of r .

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