Questions related to arithmetic progressions, which are sequences of numbers such that the difference between consecutive terms is constant

An *arithmetic progression* or *arithmetic sequence* is a sequence of numbers such that the *common difference* between consecutive terms is constant. For instance, the sequence 15, 13, 11, 9, 7, $\ldots$ is an arithmetic progression with common difference –2.

If the first term of an arithmetic progression is $a_1$, and the common difference is $d$, then the $n$th term of the sequence $(a_n)$ is $$a_n = a_1 + (n-1)d.$$

If the common difference $d$ is—

- positive, the terms increase to positive infinity.
- negative, the terms decrease to negative infinity.

A finite portion of an arithmetic progression is called a *finite arithmetic progression* or sometimes just an arithmetic progression. The sum of a finite arithmetic progression is called an *arithmetic series*.