Chapter 9.1 Introduction to Sequences Algebra II Chapter 9.1 Introduction to Sequences

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

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

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

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

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

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

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

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?

Try these! Pg. 629 #11-13

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

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

Try these! Pg. 629 #5-10, 14

1 ½ ¼ next?

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

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!

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 = ?

Recursive formula 𝑎 1 =25 𝑎 𝑛 = 𝑎 𝑛−1 −5

Try these! Pg. 629 #2-4

Homework/Classwork Pg. 629 #16-21, 23,24,27-32, 50-53 all