If the first three terms in the expansion of `(1+x)^(n)` are in A .P . , prove that,
`n(n-1)x^(2)-4nx+2=0`.

n th term in the expansion of (x+(1)/(x))^(2n)

If the first three terms in the expansion of (1+ax)^n are 1,6x and 16x^2 , find a and n

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 .

The first three terms in the expansion of (1+a x)^n are 1,12 x,64 x^2 . Find n and a.

If the first three terms in the expansion of (1+ax)^n are 1,12 x , 64x^2 , find 'n' and 'a'

If the first three terms in the expansion of (1+ax)^(n) are 1,8x,24x^(2) respectively,then a=

If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1+x)^(2n) are in A.p., then prove that 2n^2-9n+7=0 .

If the coefficients of the pth , (p+1)and (p+2) terms in the expansions of (1+x)^(n) are in A.P , show that , n^(2)-n(4p+1)+4p^(2)-2=0

If the first three terms in the expansion of (1 + ax)^(n) in ascending powers of x are 1+ 12x + 64x^(2) , find n and a .