Back to Unit 19

Modeling Sequences/algebra

Patterns and Term Tables

Patterns: One method of problem solving is to look for patterns in data. The first thing we do is set up a term table to look at the data.

Term Table: This is an organized table. It contains two main rows sometimes there is a third row, which contains a picture of the pattern:
Top Row: the term number – first term is 1; second term is 2; etc.
Bottom Row: the term – this is the actual value of each term in the sequence
Example:
 Term Number (n) 1 2 3 4 Term (t) 3 5 7 9

Step 1: Look for a pattern in the term sequence (the bottom line)

Step 2: Put it into words: in the pattern above, the term increases by two each time.

Step 3: try to relate your pattern to the term number. The term is equal to 2 times the term number plus one.

Every time there is a constant difference between term numbers, you are multiplying the term number by that difference. (in the example above, the term increased by two every time, so we multiplied the term number by two) Then determine if you have to add or subtract to get the term.
Step 4: Write an equation to represent your pattern.

An Equation is a mathematical sentence stating that two quantities are equal. We often use variables to represent unknown values in the equation.

A variable is a quantity that is unknown or changes. It is represented by a lower-case letter or a symbol.

The pattern above can be represented by the following equation:
Let t = the term
n = the term number t=2n+1

This means that when n = 1, the term is 2·1+1=3