1. Sequences Section 14.1

2. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population will be: 100,000 + 0.05(100,000) = 105,000 After the second year, the town’s population will be: 105,000 + 0.05(105,000) = 110,250 After the third year, the town’s population will be: 110,250 + 0.05(110,250) ≈ 115,763

3. Sequences If we continue to calculate, the town’s yearly population can be written as the infinite sequence of numbers 105,000, 110,250, 115,763, …. If we decide to stop calculating after a certain year (say, the fourth year), we obtain the finite sequence 105,000, 110,250, 115,763, 121,551

4. Sequences  An infinite sequence is a function whose domain is the set of natural numbers {1, 2, 3, 4, …}  Ex. 2, 4, 6, 8, …  A finite sequence is a function whose domain is the set of natural numbers {1, 2, 3, 4, …, n}, where n is some natural number.  Ex. 1, -2, 3, -4, 5

5. Writing the terms of a Sequence

6. First term Second term Third term Tenth term

7. Example 1:

10. OYO:

11. Example 2:

15. OYO:

16. Example 3: Finding the general term of a sequence

20. OYO:

21. Example 4: Application

22. OYO:

23. HOMEWORK  Unit 19 homework page (on the back of your unit plan) # 1 – 5