1. Geometric Sequences A geometric sequence is a sequence where each # in the seq. is multiplied by a constant (which is called the common ratio (r)) To find r, divide any term in the sequence by the previous term

2. Geometric Sequences General Formula:

3. Geometric Sequences Find the 11 th term of the geo. Sequence listed below 64, -32, 16, -8,…a 11

4. Geometric Sequences Find the 6 th term of the geo. sequence listed below 3, -15, 75,..a 6

5. Geometric Sequences Write an equation for the nth term 3, 12, 48, 192...a n

6. Geometric Sequences Find the 10 th term of the sequence if a 4 =108 r=3

7. Geometric Sequences Find the 7 th term of the sequence if a 3 =96 r=2

8. Geometric Means Geometric means are the missing terms between two non-successive terms in a geo. Sequence Find 3 geometric means between 2.25 and 576

9. Geometric Means Find 5 geometric means between ½ and 1/1458

10. Geometric Series A series that is associated with a geometric sequence

11. Geometric Series Find the sum of the first 6 terms of the geometric series 3 + 6 + 12 + 24 +…

12. Geometric Series Find the first term of the series if the S 8 =39,360 and r=3

13. Geometric Series Find the sum of the first 8 terms of 1+x+x 2 +x 3 +…

14. Sigma Notation More concise (less time consuming) notation for writing out a series

15. Sigma Notation

18. Write in sigma notation 1 + 3 + 5 + 7

19. Write in sigma notation 2 + 4 + 6 + 8 + 10

20. Write in sigma notation 3 + 6 + 12 + 24 + 48

21. Write in sigma notation -3 + 9 + -27 + 81 + -243

22. Write in sigma notation -2 + 4 + -8 +... +256

23. Infinite Geometric Series In an infinite series, S n approaches some limit as n becomes very large. That limit is defined to be the sum of the series. If an infinite series has a sum, it is said to converge. A series converges (or has a sum) if and only if lrl < 1

24. Does the geom. series have a sum?

26. Does the sum of each term approach some limit?

27. To find the sum of an infinite series Make sure a limit exists first

28. An infinite series in sigma notation—find the sum

30. Writing a repeating decimal as a fraction

32. A different kind of sequence...

33. Expand

34. Pascal’s Triangle 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 First row is used for anything to the zero power. Used for the coefficients of each term of the expanded binomial

35. Expand using Pascal’s Triangle