Arithmetic Sequence

A sequence where we add or subtract a constant to/from each term to get to the next term. Nice 'n' simple.

Arithmetic Series

The sum of the terms of an arithmetic sequence—that's it.

Common Difference

In an arithmetic sequences or series, it's the difference between any two terms. In other words, the number we're adding to each term.

Common Ratio

In a geometric sequence or series, it's the number used to multiply and obtain the next number in the sequence.

Convergence

The idea that the sum of an infinite series approaches a certain number as the number of terms gets bigger and biggER and biGGER and BIGGER.

Divergence

When the sum of an infinite series gets infinitely, tremendously, and insanely huge as the number of terms increases.

Explicit Rule

A general rule, or formula, that gives us the nth term of a sequence.

Factorial

The product of a number and all the numbers before it, all the way down to 1. For example, 5! would be 5 × 4 × 3 × 2 × 1.

Fibonacci Sequence

An amazingly cool sequence that's found by adding the two previous terms together to obtain the next term: 0, 1, 1, 2, 3, 5, 8, 13, and so on.

Geometric Sequence

A sequence where we multiply each term by a constant ratio to get to the next term. These guys tend to grow or shrink a lot quicker than their arithmetic cousins.

Geometric Series

The sum of the terms of a geometric sequence.

Partial Sum

The sum of the first n terms of a series—any kind of series. Seriously.

Recursive Rule

A rule (still thinking math rule here) for a sequence of numbers in which the next term is based on one or more previous terms.

Sequence

A list of numbers defined by a rule—typically ones that are math-related as opposed to, "No iPad at the dinner table."

Series

The sum of all the terms in a sequence. It's like a recipe: if a sequence is the list of ingredients, a series is the actual sum of all those ingredients.