Prove that `(2n)^2` where `n in N` can be expressed as the sum of `n` terms of a series of integers in AP

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.

Find the sum of n terms of the series whose n t h term is: 2n^2-3n+5

Find the sum of n terms of an AP where a_(n)=5-6n and n in N

Find the sum of n terms of the series whose n^(th) term is 18 n^(2) - 6n + 5

(a) The sum of 'n' terms of a progression is n(n + 1). Prove that it is an A..P. Also find its 10th term. (b) The sum of 'n' terms of a progression is (3n^(2) - 5n). Prove that it is an A.P. (c) If the sum of n terms of a series is (5n^(2) + 3n) then find its first five terms.

The sum of n terms of a series is (3n^(2)+2n) . Prove that it is an A.P.

The nth term of a series is 3^(n)+2n; find the sum of first n terms of the series.

Find the sum to n term of the series whose n^(th) term is given by n(n^(2) + 1)