Prove that the sum of n numbers between a and b such that then(a + b)resultingseries becomes A.P. is `(n(a+b))/2`

If the sum to n terms of a sequence be n^2+2n then prove that the sequence is an A.P.

If the sum to n terms of a sequence be n^(2)+2n then prove tht the sequence is an A.P.

If the sum to 'n' terms of an A.P. is (4n^(2) -2n)/( 4) then the n^( th) term of the A.P. is

The sum of first n terms of a series is n^(2) + an + b . Show that b = 0 and the series is in A.P.

Find the numbers a,b,c between 2 and 18 such that (i) their sum is 25 (ii)the numbers 2,a,b are consecutive terms of an A.P and (iii) the numbers b,c 18 are respectively terms of a G.P

If the first terms, second term and the last term of an A.P. are respectively a,b and c.Prove that the sum of the series is [(a+c)(b+c-2a)]/[2(b-a)] .

If the first,second and nth terms of a A.P. are respectively a,b and c then prove that the sum of n terms of this series is

Three numbers a, b, c are lies between 2 and 18 such that their sum is 25. 2, a, b, are in A.P, and b, c, 18 are in G.P. Then abc =

The first term, last term and common difference of an A.P. are respectively a, b and 1. Prove that the sum of this A.P. is (1)/(2)(a+b)(1-a+b) .

The first term, last term and common difference of an A.P. are respectively a, b and 1. Prove that the sum of this A.P. is (1)/(2)(a+b)(1-a+b) .