Download Section 11.1

Algebra 2B
Day 30
11.1 Patterns

Daily Openers

Go over and collect homework
11.1 Patterns
sequence – ordered list of numbers
term – each number in a sequence
Ex. You drop a super ball from a height of 12 feet. If the ball rebounds to 80% of its
previous height, how high will the ball rebound after its 5th bounce?
recursive formula – where a term in a sequence is defined by relating it to the previous term.
Ex. Describe the pattern, and write a recursive formula for the sequence:
(a) 2, 5, 8, 11, 14, …
(b) 5, 10, 20, 40, …
(c) 1, -6, 36, -216, …
Ex. In the sequence: 33, 29, 25, 21, 17, …, a1 represents the 1st term,
a2 represents the 2nd term, a3 represents the 3rd term, and so on. Find a7, a10, and a14
Ex. For the recursive formula: an  2an1  3 , where
Ex. For the recursive formula: a n 
a1  4 , find a 5 .
2
a n 1 , where a1  18 , find a 6 .
3
explicit formula – expresses the nth term in terms of n.
– you don’t need to know the previous term to find the nth term.
Ex. For the explicit formula: a n  4n  5 , find
Ex. For the explicit formula: an  3n  n , find
2
a 20
a11
Homework – page 603 #1–41 all, 46, 48
Daily Openers – Find the next three terms in the pattern:
1. 1, 1, 2, 3, 5, 8, ____ , ____ , ____
1
1
1
2. 1,
,  ,  1 , -2, ____ , ____ , ____
4
4
2
3. 0, 8, 27, 64, ____ , ____ , ____
1 1

3 6
4. Simplify:
2
3
4n 2
2n
3


5. Solve: 2
n 9 n3 n3