Ch.9 Sequences and Series

Section 4 –Arithmetic Series

Definitions:

Series: the sum of the terms of a sequence.

Finite Series: has a first and last term.

Infinite Series: Continues without end.

EXample

Finite Sequence Finite Series6,9,12,15,18 6+9+12+15+18=(60)

Infinite Sequence Infinite Series3,7,11,15,… 3+7+11+15+…

Definition: Arithmetic Series

A series whose terms form an arithmetic sequence.

Sum of a Finite Arithmetic Series

+ Where is the first term and is the nth term.

EXample

What is the sum of the even integers from 2 to 100?

EXample

A company pays a bonus to salespeople at the end of their first 50 weeks if they make 10 sales in their first week and, then improve their sales by two each week thereafter. How many sales would someone need to get the bonus?