Download 9.1 Notes.notebook - Perry Local Schools

9.1 Notes.notebook
March 17, 2014
9.1 Mathematical Patterns
Name: ____________________
Objectives: Students will be able to identify mathematical
patterns found in a sequence and use a formula to find the nth
term of a sequence.
A _________ is an ordered list of numbers. Each number in a
sequence is a _____ ___ ___ _________.
You can represent a
term of a sequence by using a variable with a subscript number to
indicate the position in the sequence.
1st term
2nd term
3rd term
4th term
a1
a2
a3
a4
Mar 11­12:57 PM
An _________ ________ describes the nth term of a sequence
using the number n.
Example A sequence has an explicit formula an = 3n - 2. What are
the first 6 terms of the sequence?
Mar 11­1:02 PM
1
9.1 Notes.notebook
March 17, 2014
Examples Write an explicit formula for each sequence. Find the
tenth term.
1.) 2, 4, 6, 8, 10, ...
2.) 4, 5, 6, 7, 8, ...
3.) 1, 4, 9, 16, ...
4.) 3, 7, 11, 15, 19, ...
Mar 11­1:11 PM
5.) 1/2, 1/3, 1/4, 1/5, ...
Sometimes you can see the pattern in a sequence by comparing
each term to the one that came before it. When this happens, we
can write a _________ ________ to represent the sequence.
A recursive defintion contains two parts:
1.) an intitial condition (the value of the first term, a1)
2.) the formula and for what n values it is defined.
A famous example is the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, ...
an = ______ + ______ for n _____.
Mar 11­1:13 PM
2
9.1 Notes.notebook
March 17, 2014
Examples Write a recursive definition for each sequence.
1.) 133, 130, 127, 124, ...
2.) 1, 2, 4, 8, 16, ...
3.) 1, -3, 9, -27, 81, ...
Mar 11­1:18 PM
Example You walk 1 mile the first days of your training, 1.2 miles
the second day, 1.6 miles the third day and 2.4 miles the fourth
day. If you continue this pattern, how many miles do you walk the
seventh day?
Mar 11­2:17 PM
3