Sequences & Series

Sequence A sequence is a special set of numbers, in which the name suggests, the order of the terms is important. The two important categories of sequences are arithmetic sequences and geometric sequences. Both are examples of recursive sequences in which each term depends on the previous term.

Recursive Formula A recursive formula is a rule in which one or more previous terms are used to generate the next term. Example: Find the first five terms of the sequence with a1 = 5 and an-1 + 1 for n ≥ 2

Explicit Formula An explicit formula defines the nth term of a sequence as a function of n. Example: Find the first five terms of the sequence an = 2n – 3

Series A series is the indicated sum of the terms of a sequence. 1,2,3,4 2,4,6,8, … ½,⅓,¼,⅕,⅙ Series 1+2+3+4 2+4+6+8+… ½+⅓+¼+⅕+⅙

Summation Notation A series can also be used by using summation notation, which uses the Greek letter ∑ (capital sigma) to denote the sum of a sequence defined by a rule.

Summation Notation