1. Coordinate Algebra Arithmetic and Geometric Sequences Learning Target: Students can use the explicit formula to find the n th term of a sequence.

2. Arithmetic Sequences (Common difference) Geometric Sequences (common ratio) Explicit Formula Recursive Formula Explicit Formula Recursive Formula

3. Each distance is 0.2 miles greater than the previous distance. Example: The distance between you and a lightning strike can be approximated by using a sequence. Times (s)Distance (mi) 10.2 20.4 30.6 40.8 51.0 61.2 71.4 81.6 *When the terms of a sequence differ by the same nonzero number d, the sequence is an arithmetic sequence and d is the common difference. A sequence is a list of numbers that may form a pattern. Each number in a sequence is called a term.

4. Arithmetic Sequence A sequence of terms that have a common difference (d) between them -Subtract terms right to left

5. 12, 8, 4, 0, … Step 1: Find the difference between successive terms. Step 2: Use the common difference to find the next 3 terms. Determine whether each sequence appears to be an arithmetic sequence. If so, find the common difference and the next three terms in the sequence. Add -4 to each term to find the next term. The sequence is arithmetic and the common difference is -4. 0-4 = -4, -4 – 4 = -8, -8 – 4 = -12

6. 1, 4, 9, 16, … Step 1: Find the difference between successive terms. The difference between successive terms is not the same, so the sequence is not arithmetic. 1 + 3 = 4, 4 + 5 = 9, 9 + 7 = 16

7. Explicit Formula for Arithmetic Sequence (Finding the nth term)

8. Explicit Formula for Arithmetic Sequences a 1 + (n-1)d = a n (Allows us to find ANY term in a sequence) a 1 1 st term a 1 = 1 st term nthe number of the term you are looking for n= the number of the term you are looking for dcommon difference d= common difference a n the value of the term that you are looking for a n = the value of the term that you are looking for

9. Geometric Sequence A sequence of terms that have a common ratio (r) between them -Divide terms right to left

10. Explicit Formula Formula used to find the n th term of a sequence

11. Explicit Formula for Geometric Sequence

12. Arithmetic or Geometric? Example : -22, -15, -8, -1, … Arithmetic d = 7

13. Arithmetic or Geometric? Example : 7, 4, 1, -2, -5 Arithmetic d = -3

14. Arithmetic or Geometric? Example : 256, 64, 16, 4, … Geometric r = 1/4

15. Arithmetic or Geometric? Example : Geometric r = 2/3

16. Find the common difference, the explicit formula, and the tenth term. 3, 9, 15, 21, … d = 6 a 10 = 57

17. Find the common ratio, the explicit formula, and the seventh term. 3, 1.5, 0.75, 0.375, …

18. The fifth term is 1,792. The constant ratio is 4. Write the explicit formula.

19. Homework Sequence Practice WS