1. Warm Up 09.08.11 Week 4 ( 2, 5 ) and ( 14, 1 ) 1) What is the midpoint?

2. Geometry Sequences Day 3 I will write a recursive formula for a sequence of numbers. Sequence An ordered list of numbers with common differences or ratios. 7, 10, 13, 16, 19,... Ex 1

3. 7, 10, 13, 16, 19,... common difference n = 4 3 Arithmetic Sequence: find the difference ( d ). Ex 1 1613tntn t n – 1 == =1613 - tntn t n – 1 - 3= tntn 3 = + tntn d = + Arithmetic Formula

4. -6, 2, 10, 18, 26,... t 4 = t 4 - 1 + 8 t 4 = t 3 + 8 t 4 = 10 + 8 t 4 = 18 Ex 2 Check + d tntn t n – 1 = 8 = d + 8 tntn t n – 1 =

5. 4, 12, 36, 108, 324,... n = 2 common ratio = 3 t n-1 tntn = 3 4 12 = 3 t n-1 tntn 124tntn t n – 1 == Geometric Sequence: find the ratio ( r ) ( ratio means quotient ). Ex 3 = r t n-1 tntn Geometric Formula

6. 2, 8, 32, 128, 512,... Ex 4 4 = r = r t n-1 tntn t n = 4t n-1 Check t 3 = 4(t 3-1 ) t 3 = 4(t 2 ) t 3 = 4(8) t 3 = 32

7. Recursive Formulas You have to know the previous number to find the next number. tntn t n – 1 d = + = r t n-1 tntn Arithmetic Geometric

8. tntn t n – 1 d = + Arithmetic 3, 10, 17, 24, 31,... d = 7 t n = t n-1 + 7

9. Geometric 3, 12, 48, 192, 768,... r = 4 t n = 4t n-1 = r t n-1 tntn

10. Do: 1 What is the recursive formula for this sequence? Assignment: Handouts – 1.2 Recursive Formulas Part 2 -6, 1, 8, 15, 22,... - HW Part 2 - Recursive Formulas