Context: The sum to n terms of an arithmetic progression is 5n2 +2n. Find the nth term of the series.a.10n - 3b.10n + 5c.5n - 1d.5n - 2 Answer question

The sum to n terms of an arithmetic progression is given by the formula Sn = n/2 [2a + (n-1)d], where a is the first term and d is the common difference. However, in this case, we are given the sum to n terms as 5n^2 + 2n.

To find the nth term of the series, we need to find the nth term of the sum (Tn), which is the difference between the sum to n terms and the sum to (n-1) terms.

So, Tn = Sn - S(n-1) = [5n^2 + 2n] - [5(n-1)^2 + 2(n-1)]

Solving this, we get:

Tn = 5n^2 + 2n - [5(n^2 - 2n + 1) + 2n - 2] = 5n^2 + 2n - 5n^2 + 10n - 5 - 2n + 2 = 10n - 3

So, the nth term of the series is 10n - 3. Therefore, the answer is a.10n - 3.