Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April...
Transcript of Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April...
Untitled.notebook
1
April 23, 2014
Sequences & Series Introduction
Untitled.notebook
2
April 23, 2014
The petals of a flower are as follows:
1, 1, 2, 3, 5, 8, 13, …
Can you find the next four values?
Untitled.notebook
3
April 23, 2014
Sequence• An ordered list of numbers called Terms
• Infinite Sequence – continues without end.
• Finite Sequence – has a last term
• Terms represented by t :
Untitled.notebook
4
April 23, 2014
Explicit Formula
• Formula that defines the nth term.
Untitled.notebook
5
April 23, 2014
Write the first four terms of the sequence defined by the explicit formula :
n
t
Untitled.notebook
6
April 23, 2014
Write the first four terms of the sequence defined by the explicit formula :
n
t
Untitled.notebook
7
April 23, 2014
Write the first four terms of the sequence defined by the explicit formula :
n
t
Untitled.notebook
8
April 23, 2014
Recursive Formula• One or more previous terms are
used to generate the next term.
• Find the next three terms:• 4, 7, 10, 13, 16,
• 2, 6, 18, 54,
• 1, 4, 9, 16,
Untitled.notebook
9
April 23, 2014
Write the first four terms of the sequence defined by the recursive formula :
n
t
Untitled.notebook
10
April 23, 2014
Write the first four terms of the sequence defined by the recursive formula :
n
t
Untitled.notebook
11
April 23, 2014
Back to the petals of a flower:
1, 1, 2, 3, 5, 8, 13, …
Can you write a recursive formula for this?
Untitled.notebook
12
April 23, 2014
Write a recursive formula for the sequence shown below and find the next three terms.
2, 8, 14, 20, 26, …
Untitled.notebook
13
April 23, 2014
Write a recursive formula for the sequence shown below and find the next three terms.
7, 11, 15, 19, …
Untitled.notebook
14
April 23, 2014
Write a recursive formula for the sequence shown below and find the next three terms.
2, 7, 22, 67,…
Untitled.notebook
15
April 23, 2014
Write a recursive formula for the sequence shown below and find the next three terms.
5, 9, 17, 33….
Untitled.notebook
16
April 23, 2014
Series
• Expression that indicates the sum of the terms of a sequence.
• We summation notation: Greek letter sigma
Untitled.notebook
17
April 23, 2014
“the sum of 2n for values of n from 1 to 5”
Untitled.notebook
18
April 23, 2014
Write the terms of each series. Then evaluate.
Untitled.notebook
19
April 23, 2014
Write the terms of each series. Then evaluate.
Untitled.notebook
20
April 23, 2014
Homework