if the coefficients of `x,x^2 and x^3` in the binomial expansion `(1+x)^(2n)` are in arithmetic progression then prove that `2n^2-9n+7=0`

If the coefficients of x^9, x^10, x^11 in the expansion of (1+x)^n are in arithmetic progression then n^2=41n=

If the coefficients of x, x^2 and x^3 in the binomial expansion of (1+x)^(2n) are in A.P., prove that 2n^2-9n+7=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

The coefficients fo x^(n) in the expansion of (1+x)^(2n) and (1+x)^(2n-1) are in the ratio

The coefficients of x^(n) in the expansion of (1+x)^(2n) and (1+x)^(2n-1) are in the ratio