1. Math II UNIT QUESTION: How is a geometric sequence like an exponential function? Standard: MM2A2, MM2A3 Today’s Question: How do you recognize and write rules for number patterns? Standard: MM2A3d

2. Section 4.7 Sequences & Series

3. Sequence A sequence is a set of numbers in a specific order Infinite sequence Finite sequence

4. Sequences – sets of numbers

5. Ex. 1 Find the first four terms of the sequence First term Second term Third term Fourth term

6. Ex. 2 Find the first four terms of the sequence

7. Writing Rules for Sequences We can calculate as many terms as we want as long as we know the rule or equation for a n. Example: 3, 5, 7, 9, ___, ___,……. _____. a n = 2n + 1 a n = a 1 + (n-1)d

8. Writing Rules for Sequences Try these!!! 3, 6, 9, 12, ___, ___,……. _____. 1/1, 1/3, 1/5, 1/7, ___, ___,……. _____. a n = 3n, a n = 1/(2n-1)

9. Series – the sum of a certain number of terms of a sequence “Add up the terms in the sequence beginning at term number 1 and going through term number “n”. Start Stop Formula

11. Infinite Sequence Infinite Series Finite Seriesor nth Partial Sum

12. Series Notation Practice Workbook Page 155 #19-24

13. Arithmetic Series

14. The sum of the terms in a sequence are called a series. There are two methods used to find arithmetic series: Formula Sigma Notation

15. Arithmetic Series SequenceSumAverageAvg. x n 2, 5, 8, 11, 14 408 1, 8, 15, 22 4623/246 -1,1, 3313 What’s another way to get the average without adding all the numbers and dividing by n?

16. Arithmetic Series a 1 = first term n = number of terms a n = value of the nth term In many problems, you will first have to use the arithmetic sequence formula.

17. Arithmetic Series Find the sum of the arithmetic series. 648

18. Arithmetic Series Find the sum of the arithmetic series. 10,100

19. Arithmetic Series Find a formula for the partial sum of this series: 1+3+5+....+(2n-5)+(2n-3)+(2n-1)