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)-on(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

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

The ratio of the coefficient of terms (x^(n-r)a^(r) and x^(r)a^(n-r) is the binomial expansion of (x+a)^(n) will be:

If the coefficients of the 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

If the coefficients of rth, (r+ 1)th and (r + 2)th terms in the expansion of (1 + x)^(1//4) are in AP, then r is /are

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.