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`

If the coefficient of (3r)^(th) and (r + 2)^(th) terms in the expansion of (1 + x)^(2n) are equal then n =

If the coefficient of (2r + 4)^(th) term and (r - 2)^(th) term in the expansion of (1 + x)^18 are equal then find r.

If the coefficients of (2r + 1)th term and (r + 2)th term in the expansion of (1 + x)^(48) are equal,find r .

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 coefficients of rth, (r + 1)th and (r + 2)th terms in the expansion of (1 + x)^n be in H.P. then prove that n is a root of the equation x^2 - (4r - 1) x + 4r^2 = 0.

If the coefficients of r^(th) , (r + 1)^(th) and (r + 2)^(th) terms in the binomial expansion of (1 + y)^m are in A.P. then find the equation m and r satisfy

If the coefficients of (2r+4)^("th") term and (3r+4)^("th") term in the expansion of (1+x)^(21) are equal, find r.

The coefficients of the (r-1)^(th),r^(th) and (r+1)^(th) terms in the expansion of (x+1)^n are in the ratio 1:3:5 .Find n and r.

If the coefficient of (2r+4)th and (r-2)th terms in the expansion of (1+x)^(18) are equal, find r .

If the coefficients of (2r + 4)th, (r - 2)th terms in the expansion of (1 + x)^18 are equal, find r.