Any odd square 1.e. `(2n + 1)^2` is equal to sumterms of an A.P. increased by unity.

Prove that square of any even natural number i.e. (2n)^2 is equal to sum of n terms of a certain series of integers in A.P.

If the sum of the first 2n terms of the A.P. 2, 5, 8, ..., is equal to the sum of the first n terms of A.P. 57, 59, 61. .... then n equals

If the sum of the first 2n terms of the A.P. 2, 5, 8, ..., is equal to the sum of the first n terms of A.P. 57, 59, 61, ..., then n equals

If the middle term amongst any odd number (n) consecutive terms of an A.P, is m, then their sum is (a) 2m^2n (b) (mn)/2 (c) mn (d) mn^2

If the sum of the first 2n terms of the A.P. 2,5,8, "……….." is equal to the sum of the first n terms of the A.P. 57,59,61, "…………" then n equals :

If the n^(t h) term of an A.P. is 2n+1 , then the sum of first n terms of the A.P. is n(n-2) (b) n(n+2) (c) n(n+1) (d) n(n-1)

If the n^(t h) term of an A.P. is 2n+1 , then the sum of first n terms of the A.P. is n(n-2) (b) n(n+2) (c) n(n+1) (d) n(n-1)

The sum of the first n terms of the A.P 3, 5 1/2, 8,... is equal to the 2n^(th) term of the A.P 16 1/2, 28 1/2, 40 1/2,... . Calculate n

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