SEQUENCES OBJECTIVES: Write the first several terms of a sequence Write the terms of a sequence defined by a Recursive Formula Use Summation Notation Find the Sum of a Sequence

S EQUENCES Infinite sequence: is a function whose domain is the set of positive integers. The function values, or terms, of the sequence are represented by Finite sequence: sequences whose domains consist only of the first positive integers The letter with a subscript is used to represent function values of a sequence, rather than the usual function notation. The notation represents the nth term, or general term, of a sequence.

EX 1: W RITE THE FIRST FIVE TERMS OF A SEQUENCE FROM THE GENERAL TERM A) B)

EX 2: W RITE DOWN THE NTH TERM OF EACH SEQUENCE A) B)

R ECURSIVE FORMULA Recursive Formula: defines the nth term of a sequence as a function of the previous term or terms and specifies the nth term by a formula or equation that involves one or more of the terms preceding it. is the first term is the previous term

EX 3: W RITE THE FIRST FIVE TERMS OF A SEQUENCE DEFINED RECURSIVELY A) B) C)

S UMMATION N OTATION Summation Notation: the sum of the first terms of a sequence is represented by the summation notation where is the index of summation, is the upper limit of summation, and 1 is the lower limit of summation. Expanding the summation notation is when we write out a sum that is given in summation notation.

EX 4: W RITE OUT EACH SUM A) B)

EX 5: EXPRESS EACH SUM USING SUMMATION NOTATION A) B)