Arithmetic Series Definitions & Equations Writing & Solving Arithmetic Series Practice Problems

Definitions 2  Series  The sum of terms in a sequence  Arithmetic Series  The sum of terms in an arithmetic series  Sigma ( S )  The Greek symbol for the letter “S”  Indicates addition of terms

Arithmetic Series  Addition of terms in an arithmetic sequence Arithmetic SequenceArithmetic Series or 3

Finding the Sum of an Arithmetic Series  Find the sum of the first 100 positive integers Method 1Method 2 4

Finding the First Term  A radio station considered giving away $4,000 every day in the month of August for a total of $124,000. Instead, they decided to increase the amount given away everyday, while still giving away the same total amount. If they want to increase the amount by $100 each day, how much should they give away the first day? 5

Finding the First Term 31 days in August, n=31 6

Finding the First 3 Terms  Find the first three terms of an arithmetic series in which a 1 =9, a n =105, and S n =741. 7

Finding the First 3 Terms 8

Sigma Notation  Writing out a series can be time-consuming. For convenience, there is an abbreviated method called sigma notation. a = the first value of nb = the last value of n f(x) = the formula “n” is called the index of summation 9

Sigma Notation Example  Write a sigma notation for the series …+30 Since each term advanced by 3 and started with 3, the function is 3n. As there are 10 terms in the sequence, the first value of n is 1 and the last is

Evaluating a Sum in Sigma Notation Evaluate Method 1Method 2 11