In this unit, students apply their skills using tables, equations, and graphs to identify patterns and learn about sequences. A sequence is a list of numbers, and each number in a sequence is called a term. If you have ever used “fill down” to continue a pattern in a spreadsheet, you have created a sequence. For each sequence of numbers here, can you figure out how to find the next number?

sequence : 4, 7, 10, 13,

sequence : 2, 6, 18, 54,

You probably noticed that, for sequence , you can add 3 to any term to get the next term. There are different ways we could represent this sequence.

Using words:

“To find the  term, multiply by 3 and add 4.”

Using notation for defining a function:

(the value of the  term is ). For example, , so (the value of the 2nd term is 10).

Here is a task to try with your student:

Let’s revisit sequence : 2, 6, 18, 54, . . .

1. What do you notice about the sequence?
2. If the pattern is “multiply any term by 3 to get the next term,” what is the next term?
3. If we call 2 the “0th term,” what is the 10th term?
4. How could we express the  term?
5. Represent sequence in as many different ways as you can.

Solution:

1. Students may notice:
   1. All the numbers are even.
   2. The values of the terms are increasing.
   3. Each term is 3 times the value of the previous term.
2. 162
3. 118,098
4. . This can also be written or .
5. Here are some ways:

   position in list	0	1	2	3
   term	2	6	18	54

   

   “Multiply any term by 3 to get the next term.”