Suppose that `a_1,a_2,....,a_n,....` is an A.P. Let `S_k=a_((k-1)n+1)+a_((k-1)n+2)+......+a_(kn).` Prove that `S_1, S_2,... `are in A.P. having common difference equal to `n_2` times the common differ-ence of the A.P. `a_1,a_2,...`

We know that, if a_1, a_2, ..., a_n are in H.P. then 1/a_1,1/a_2,.....,1/a_n are in A.P. and vice versa. If a_1, a_2, ..., a_n are in A.P. with common difference d, then for any b (>0), the numbers b^(a_1),b^(a_2),b^9a_3),........,b^(a_n) are in G.P. with common ratio b^d. If a_1, a_2, ..., a_n are positive and in G.P. with common ration, then for any base b (b> 0), log_b a_1 , log_b a_2,...., log_b a_n are in A.P. with common difference logor.If x, y, z are respectively the pth, qth and the rth terms of an A.P., as well as of a G.P., then x^(z-x),z^(x-y) is equal to

Let a_1, a_2, a_3, ...a_(n) be an AP. then: 1 / (a_1 a_n) + 1 / (a_2 a_(n-1)) + 1 /(a_3a_(n-2))+......+ 1 /(a_(n) a_1) =

If a_1,a_2,a_3,...,a_(n+1) are in A.P. , then 1/(a_1a_2)+1/(a_2a_3)....+1/(a_na_(n+1)) is

The sixth term of an A.P.,a_(1),a_(2),a_(3),.........,a_(n) is 2. If the quantity a_(1)a_(4)a_(5), is minimum then then the common difference of the A.P.

"If "a_1,a_2,a_3,.....,a_n" are in AP, prove that "a_(1)+a_(n)=a_(r)+a_(n-r+1)""

Let a_1,a_2 ,a_3 ...... be an A.P. Prove that sum_(n=1)^(2m)(-1)^(n-1)a_n^2=m/(2m-1)(a_1^2-a_(2m)^2) .

A sequence a_n , n in N be an A.P. such that a_7 = 9 and a_1 a_2 a_7 is least, then the common difference is:

A sequence a_n , n in N be an A.P. such that a_7 = 9 and a_1 a_2 a_7 is least, then the common difference is:

Let (1+x^2)^2 (1+x)^n= A_0 +A_1 x+A_2 x^2 + ...... If A_0, A_1, A_2,........ are in A.P. then the value of n is

If a_1,a_2,……….,a_(n+1) are in A.P. prove that sum_(k=0)^n ^nC_k.a_(k+1)=2^(n-1)(a_1+a_(n+1))