Download 4.5 Find a Pattern in a Sequence

4.5 Notes
November 09, 2011
4.5 Find a Pattern in a Sequence
Warm Up
Find the output for each input value.
4.5 Notes
November 09, 2011
4.5 Find a Pattern in a Sequence
Learn to find patterns to complete sequences
using function tables.
Vocabulary...
sequence
term
arithmetic sequence
geometric sequence
4.5 Notes
November 09, 2011
A sequence is an ordered list of numbers. Each number
in a sequence is called a term.
When the sequence follows a pattern, the terms in the
sequence are the output values of a function, and the
value of each number depends on the number’s place in
the list.
You can use a variable such as n, to represent a
number’s position in a sequence.
4.5 Notes
November 09, 2011
In an arithmetic sequence, the same value is added
each time to get the next term in the sequence.
2, 4, 6, 8, 10, 12
rule = +2
In a geometric sequence, each term is multiplied by
the same value to get the next term in the sequence.
7, 14, 21, 28, 25 42
rule = x6
4.5 Notes
November 09, 2011
Example 1A: Identifying Patterns in a Sequence
Tell whether the sequence of y-values is arithmetic
or geometric. Then find y when n = 5.
The pattern (rule) for the sequence is... __________
The type of sequence is...
arithmetic or geometric
4.5 Notes
November 09, 2011
Example 1B: Identifying Patterns in a Sequence
Tell whether the sequence of y-values is arithmetic
or geometric. Then find y when n = 5.
The pattern (rule) for the sequence is... __________
The type of sequence is...
arithmetic or geometric
4.5 Notes
November 09, 2011
Check It Out: Example 1A
Tell whether the sequence of y-values is arithmetic
or geometric. Then find y when n = 5.
The pattern (rule) for the sequence is... __________
The type of sequence is...
arithmetic or geometric
4.5 Notes
November 09, 2011
Tell whether the sequence of y-values is arithmetic
or geometric. Then find y when n = 5.
The pattern (rule) for the sequence is... __________
The type of sequence is...
arithmetic or geometric
4.5 Notes
November 09, 2011
Example 2A: Identifying Functions in Sequences
Write a function that describes the sequence.
3, 6, 9, 12,…
Make a function table.
n
Rule
y
1
3
2
6
3
9
4
12
The function y = ______ describes this sequence.
4.5 Notes
November 09, 2011
Example 2B: Identifying Functions in Sequences
Write a function that describes the sequence.
4, 7, 10, 13,…
Make a function table.
n
Rule
y
1Make a function table.
4
2
7
3
10
4
13
The function y = ______ describes this sequence.
4.5 Notes
November 09, 2011
Check It Out: Example 2A
Write a function that describes the sequence.
5, 6, 7, 8,…
Make a function table.
n
Rule
y
1
5
2
6
3
7
4
8
The function y = ______ describes this sequence.
4.5 Notes
November 09, 2011
Check It Out: Example 2B
Write a function that describes the sequence.
3, 4, 5, 6,…
Make a function table.
n
Rule
y
7
3
8
4
9
5
10
6
The function y = ______ describes this sequence.
4.5 Notes
November 09, 2011
Lesson Quiz
Tell whether each sequence of y-values is arithmetic
or geometric. Write a function that describes each
sequence, and then find y when n = 5.
1. 6, 12, 18, 24,…
2. –3, –2, –1, 0,…
3. 24, 21, 18, 15,…