Sequences & Series Section 13.1 & 13.2

Sequences A sequence is an ordered list of numbers, called terms. The terms are often arranged in a pattern.

An infinite sequence (indicated by …) can be defined by a function whose domain is the set of all natural numbers and a finite sequence can be defined by a function whose domain is the first n numbers. Each member of the range of a sequence is a term of the sequence.

Explicit Formula A formula that defines the nth term, or general term, is called an explicit formula. With this formula, each term of the sequence can be found by substituting the number of the term for n.

Example Write the first six terms of the sequence defined by the explicit formula:

Example Write the first six terms of the sequence defined by the explicit formula:

Recursive Formula A sequence can also be defined by a recursive formula. With a recursive formula, one or more previous terms are used to generate the next term.

Fibonacci Sequence The Fibonacci Sequence, also called the golden spiral, has been used to study animal populations, relationships between elements in works of art, and various patterns in plants, such as sunflowers. -sequence.html

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Series A series is an expression that indicates the sum of the terms of a sequence. For example, if you add the terms of the sequence 2, 4, 6, 8, 10, the resulting expression is the series

Summation Notation Summation notation is a way to express a series in abbreviated form. For example:

Write the terms of each series and then evaluate.

Summation Properties

Constant Series Formula

Linear Series Formula

Quadratic Series Formula

Examples

Assignment Pg. 696 #42 – 65 all