Understanding Sequences and Series

A sequence is an ordered list of numbers that follow a specific pattern or rule.

A series is the sum of the terms of a sequence.

The first term is 1.

The second term is 3.

The common difference is the constant amount added to each term to get the next term.

The formula is $$a_n = a_1 + d(n-1)$$ where $$a_1$$ is the first term, $$d$$ is the common difference, and $$n$$ is the term number.

The first term is -5.

The common difference is 2.

The formula is $$S_n = \frac{n}{2} (a_1 + a_n)$$ where $$S_n$$ is the sum, $$a_1$$ is the first term, and $$a_n$$ is the nth term.

A geometric sequence is a sequence where each term is found by multiplying the previous term by a constant called the common ratio.