Show that no three consecutive binomial coefficients can be in (i) G.P., (ii) H.P.

Statement 1: Three consecutive binomial coefficients are always in A.P.Statement 2: Three consecutive binomial coefficients are not in H.P.or G.P.

The ratio of three consecutive binomial coefficients in the expansion of (1+x)^n is 2:5:12 . Find n.

Show that the roots of the equation ax^2+2bx+c=0 are real and unequal whre a,b,c are the three consecutive coefficients in any binomial expansion with positive integral index.

If the square of differences of three numbers be in A.P., then their differences re in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If the four consecutive coefficients in any binomial expansion be a, b, c, d, then prove that (i) (a+b)/a , (b+c)/b , (c+d)/c are in H.P. (ii) (bc + ad) (b-c) = 2(ac^2 - b^2d)

If the four consecutive coefficients in any binomial expansion be a,b,c and d then (A) (a+b)/a,(b+c)/b,(c+d)/c are in H.P. (B) (bc+ad)(b-c)=2(ac^2-b^2d) (C) b/a,c/b,d/c are in A.P. (D) none of these

Let a,b,c,d be the foru cosecutive coefficients int eh binomial expansion (1+x)^n On the basis of above information answer the following question: a/(a+b), b/(b+c), c/(c+d) are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If a,b,c be 7 th 11 th and 13 th terms respectively of a non constant A.P.If these are also the three consecutive terms of a G.P the sum of infinite terms of this G.P is Ka then K=?