# Algebra II Terms

## Get down with the lingo

### 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*n*th 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.### People who Shmooped this also Shmooped...

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