Explanation of nth term of the series
The given series has a sum to n terms of 5n^2 + 2n. We need to find the nth term of this series.

Deriving the formula for nth term
To find the nth term of the series, we first need to find a general formula for the sum of the series to n terms. The sum of an arithmetic series can be expressed as Sn = n/2 [2a + (n-1)d], where a is the first term, d is the common difference, and n is the number of terms.
In this case, the sum to n terms is given as 5n^2 + 2n. Comparing this with the formula for the sum of an arithmetic series, we have:
5n^2 + 2n = n/2 [2a + (n-1)d]
Simplifying this equation, we get:
5n^2 + 2n = n(a + (n-1)d)
Now, we need to solve for a and d to find the nth term of the series.

Finding the nth term
By comparing the equation above with the general form of the nth term of an arithmetic series, an = a + (n-1)d, we can determine that a = 10 and d = -3.
Therefore, the nth term of the series is given by:
an = 10 + (n-1)(-3)
= 10 - 3n + 3
= 10n - 3
Hence, the nth term of the series is 10n - 3.