# Arithmetic Series The sum of first $n$ terms of an arithmetic sequence can be calculated like: $\sum_{k=1}^n a_n = \frac{n}{2}(2a_1+d(n-1))$ ^3b0qf5 This formula can be applied to easily calculate the sums of first $n$ odd and even numbers. See [[The Trick for Quickly Calculating the Sum of First N Odd Integers]] and [[The Trick for Quickly Calculating the Sum of First N Even Integers]]. [[The Gauss Trick]] is a version of this formula, where the sequence is the sequence of integers (i.e. $d=1$ and $a_1=1$).