The nth term of the series whose sum to n terms is 5n^2+2n Related: Sequence and Series?

Question

The nth term of the series whose sum to n terms is 5n^2+2n Related:  Sequence and Series?

Answer

Explanation:

The sum to n terms of a series can be represented by the formula:

Sn = a(1) + a(2) + a(3) + ... + a(n-1) + a(n)

To find the nth term of the series, we need to use the formula:

a(n) = Sn - Sn-1

Solution:

Given, the sum to n terms of the series is 5n^2 2n

So, we have:

Sn = 5n^2 + 2n

Using the formula, we get:

a(n) = Sn - Sn-1

a(n) = (5n^2 + 2n) - (5(n-1)^2 + 2(n-1))

a(n) = 5n^2 + 2n - 5(n^2 - 2n + 1) - 2n + 2

a(n) = 5n^2 + 2n - 5n^2 + 10n - 5 - 2n + 2

a(n) = 8n - 3

Therefore, the nth term of the series is 8n - 3.