Prove that the sum of n numbers between ...

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`

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Prove that the sum of n number of terms of two different A.P.s can be same for only one value of n.

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

Knowledge Check

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 =

A

360

B

420

C

480

D

540

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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

The sum of the first n terms of an A.P. is 3n^2+6n . Find the n t h term of this A.P.

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 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

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, l and 1. Prove that the sum of this A.P. is (1)/(2)(a+b)(1-a+b).

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