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Unit 1, Lesson 6

Representing Sequences

Algebra 2

6.1

Warm-up

For each sequence shown, find either the growth factor or rate of change. Be prepared to explain your reasoning.

5, 15, 25, 35, 45, . . .
Starting at 10, each new term is less than the previous term.
Graph, origin “O”. Horizontal axis,"term number," with scale from 0 to 6, by 1’s. Vertical axis, "value," with scale 0 to 16, by 2’s. Coordinates plotted (1 comma 16), (2 comma 8), (3 comma 4), (4 comma 2), and (5 comma 1).

for
1 0

2 0.1

3 0.2

4 0.3

5 0.4

Student Lesson Summary

Here are some ways to represent a sequence. Each representation gives a different view of the same sequence.

List of terms: Here’s a list of terms for an arithmetic sequence : 4, 7, 10, 13, 16, . . . We can show this sequence is arithmetic by noting that the difference between consecutive terms is always 3, so we can say this sequence has a rate of change of 3.

Table A: A table lists the term number and value for each term . It can sometimes be easier to detect or analyze patterns when using a table.


1	4
2	7
3	10
4	13
5	16

Graph: The graph of a sequence is a set of points, because a sequence is a function whose domain is a part of the integers. For an arithmetic sequence, these points lie on a line since arithmetic sequences are a type of linear function.

<p>Graph of a sequence D on coordinate grid.</p>

Equation: We can define sequences recursively, using function notation to make an equation. For the sequence 4, 7, 10, 13, 16, . . . , the starting term is 4, and the rate of change is 3, so for . This type of definition tells us how to find any term if we know the previous term. It is not as helpful in calculating terms that are far away, like . Some sequences do not have recursive definitions, but geometric and arithmetic sequences always do.