1. Last Time Arithmetic SequenceArithmetic Series List of numbers with a common difference between consecutive terms Ex. 1, 3, 5, 7, 9 Sum of an arithmetic sequence Ex. 1 + 3 + 5 + 7 + 9 To find the nth term in an arithmetic sequence we use To find the sum of a finite arithmetic series we use

2. Sequence Vs. Series Is it an arithmetic sequence or an arithmetic series? What is the common difference (d)? 81 + 83 + 85 + 87 +... 8, 12, 16, 20, … 4 + -3 + -10 + -17 + …

3. Section 11.3 Geometric Sequences and Series

4. Learning goals ●Geometric Sequence ●Find the nth Term ●Geometric Series ●Find the Sum

5. Ex. 2, 4, 8, 16, … r = r = Geometric Sequence Geometric Sequence has a constant (r) that when you multiply a term by r you get the next term in the sequence. We call r the common ratio

6. Write out the next 3 terms in the geometric sequence Write the first 3 terms out a 1 is our first term

7. Are the following sequences geometric or arithmetic or neither? 1, 2, 4, -8, … 1, 7, 13, 19, 25, … 81, 27, 9, 3, 1, …

8. 81, 27, 9, 3, 1, … r = to find a 6, a 12, a n we can use the equation

9. Find a n of

10. Geometric Series Add the terms of a geometric sequence to get a geometric series To find the sum of the first n terms we use:

11. Find the S 6 of 1 + 5 + 25 + 125 + 625 + …

12. Find.

13. Find n such that S n = 341 of the geometric series 1 + 4 + 16 + 64 + …

14. Summary Geometric SequenceGeometric Series Sequence where you multiply a term by r to get the next term Ex. 1, 3, 9, 27, 81 Sum of a geometric sequence Ex. 1 + 3 + 9 + 27 + 81 To find the nth term in a geometric sequence we use To find the sum of a finite geometric series we use