1. Chapter 9.1 Introduction to Sequences
Algebra II
Chapter 9.1
Introduction to Sequences

2. Warm Up
Simplify #1 −1 8 #2 (11) 2 #3 −9 3 #4 3 4

3. More Warming
Evaluate each expression for x=4 #5 2𝑥+1 #6 0.5𝑥+1.5 #7 𝑥 2 −1 #8 2 𝑥 +3

4. Sequence-ordered set of numbers
Term (of a sequence)- each number in the sequence
Infinite sequence- sequence that continues without end
Finite sequence- sequence with a limited number of terms

5. Finding a rule for a sequence
Sequence- 2,4,6,8… n=1→2 n=2 →4 n=3 →6 n=4 →8 There is a common difference of 2 Rule 𝑎 𝑛 =2n

6. Sequence 10,13,16,19…
n=1 →10
n=2 →13
There is a common difference of 3
Rule 𝑎 𝑛 =3n + ?

7. Sequence 26,22,18,14…
n=1 →26
n=2 →22
There is a common difference of _____
Rule 𝑎 𝑛 = ?

8. Sequence 26,22,18,14…
n=1 →26
n=2 →22
There is a common difference of _____
Rule 𝑎 𝑛 = ?

10. Explicit Rule- a rule that works using the number of the term as n
Explicit Rule- a rule that works using the number of the term as n. When n=1→ 11 𝑛=2→13 𝑛=3→15 etc. What rule would give you these numbers?

11. Try these!
Pg #11-13

12. Explicit formula-defines the nth term of a sequence as a function of n
Write the 6th term of the sequence where 𝑎 𝑛 = 2 𝑛 −2
𝑎 6 = 2 6 −2= 62

13. If you are given the explicit function, you can plug in any value for n to get that number term.

14. Try these!
Pg #5-10, 14

15. ½ ¼ next?

16. Fibonacci sequence
This is a well known
sequence.
Next number?

17. Recursive formula- rule in which one or more previous terms are used to generate the next term
n refers to the term number
𝑎 𝑛 refers to the term value
YOU MUST KNOW THE 1ST TERM AND THE RULE TO USE THIS FORMULA!

18. Finding terms in a recursive formula
𝑎 𝑛−1 refers to the previous term
Find the first five terms
𝑎 1 =7 𝑎𝑛𝑑 𝑎 𝑛 =3 𝑎 𝑛−1 −4
𝑎 2 =3 7 −4=17
𝑎 3 =3 17 −4= ?
𝑎 4 =3 𝑎 3 −4= ?
𝑎 5 = ?

19. Recursive formula
𝑎 1 = 𝑎 𝑛 = 𝑎 𝑛−1 −5

20. Try these!
Pg #2-4

21. Homework/Classwork
Pg. 629 #16-21, 23,24,27-32, all