1. Analyzing Arithmetic Sequences and Series Section 8.2 beginning on page 417

2. Identifying Arithmetic Sequences Arithmetic. Not Arithmetic.

3. Writing Rules for Arithmetic Sequences The common difference For example, the equation for the nth term of an arithmetic sequence with a first term of 3 and a common difference of 2 is given by:

4. Writing a Rule

5. Writing a Rule Given an Term and the Common Difference 123456 9630-3-6

6. Writing a Rule Given Two Terms Subtract the second equation from the first. Find d.

7. Finding Sums of Finite Arithmetic Series The expression formed by adding the terms of an arithmetic sequence is called an arithmetic series. The sum of the first n terms of a finite arithmetic series can be found using the following formula. ** notice that the sum of the terms is the average of the first and last terms multiplied by the number of terms.

8. Continued… Example 5: Find the sum FIRST: Find the first and last terms:SECOND: Find the sum using the formula.

9. Solving a Real-Life Problem Example 6: You are making a house of cards similar to the one shown. a) Write a rule for the number of cards in the nth row when the top row is row # 1. b) How many cards do you need to make a house of cards with 12 rows? Row 1: Row 2: Row 3: 3 cards 6 cards 9 cards You would need 234 cards to make a house of cards with 12 rows.

10. Monitoring Progress Arithmetic, d=3Arithmetic, d=-6Not arithmetic, the differences are not constant

11. Monitoring Progress Find the sum. 7) 8)9) 10) What if, in example 6,how many cards do you need to make a house of cards with 8 rows? Row 1: Row 2: Row 3: 3 cards 6 cards 9 cards