The sum of the first n terms of an arithmetic sequence is Sn=3n^2 - 2n. How can you find the formula for the nth term un in terms of n?

Having learned a lot about the arithmetic and geometric sequences, most people are used to expressing the n^th term of a sequence un in the form u_n=u₁+d(n-1) for the arithmetic sequence and u_n=u₁*r^n-1 for the geometric sequence. However, there are some sequences for which it is hard to tell whether they are geometric or arithmetic (as the one described above), and yet, there are methods of finding the expression for their n^th term without the need to do it.
We know that S_n=u₁+u₂+...+u_n. But also S_n-1=u₁+u₂+...+u_n-1. Hence, to find the expression for u_n it is sufficient to compute the value of S_n-S_n-1! S_n-S_n-1= 3n² - 2n - 3(n-1)² + 2(n-1) = 3n² - 2n - 3(n² - 2n + 1) + 2n - 2 = 3n² - 2n - 3n² + 6n - 3 + 2n - 2 = 6n - 5. Hence u_n = 6n - 5.