explicit formula ­ day 1.notebook
March 03, 2016
Topic: Sequences
Aim: How do we determine if a sequence is arithmetic or
geometric? How can we write an explict formula to find the
nth term?
Do Now: Find the next 3 terms in each sequence:
1) 4, 7, 10, 13, ____, ____, _____,...
2) 3, 9, 27,_____, ______, ______,...
Feb 11­9:48 PM
Feb 11­10:01 PM
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explicit formula ­ day 1.notebook
March 03, 2016
Feb 11­10:03 PM
Find the common difference or ratio of each sequence.
Place each of the given 6 sequences below into the proper
column.
Arithmetic
4, 7, 10, 13, ...
­18, ­13, ­8, ­3, ...
5, 10, 15, 20, ...
Geometric
10, 20, 40, 80, ...
3, 9, 27, 81, ...
24, 12, 6, 3, ...
Feb 11­10:04 PM
2
explicit formula ­ day 1.notebook
March 03, 2016
1) What is the 10th term in the following sequence?
7, 10, 13, 16,....
What is the 99th term? (Do we really want to continue writing terms until
we reach the 99th?)
Feb 11­10:30 PM
Arithmetic
Explicit formula
an = a1 + (n-1)d
Geometric
Explicit formula
an = a1 rn-1
Feb 11­10:35 PM
3
explicit formula ­ day 1.notebook
Arithmetic
Explicit formula
an = a1 + (n-1)d
March 03, 2016
Geometric
Explicit formula
an = a1 rn-1
Let's go back to the first example.
1) Write an explicit formula for the following sequence.
5, 10, 15, 20,....
What is the 99th term?
Feb 12­12:18 PM
Arithmetic
Explicit formula
an = a1 + (n-1)d
Geometric
Explicit formula
an = a1 rn-1
Feb 11­10:34 PM
4
explicit formula ­ day 1.notebook
March 03, 2016
Feb 12­12:34 PM
4.
Feb 12­5:24 PM
5
explicit formula ­ day 1.notebook
March 03, 2016
Feb 12­5:24 PM
6.
Feb 12­5:25 PM
6
explicit formula ­ day 1.notebook
March 03, 2016
Summary: How do we determine if a sequence
is arithmetic or geometric?
How can we write an explict formula to find the
nth term?
Feb 12­12:31 PM
7