7th Grade Math

Get ConnectED

Patterns

PART B C

Multi-Part

Lesson 2

A

SPI 0706.1.2

Generalize a variety of

patterns to a symbolic rule

from tables, graphs, or

words. Also addresses

GLE 0706.1.4, GLE 0706.1.5,

GLE 0706.1.7.

44 Expressions and Patterns

Sequences

Use

centimeter cubes to make the

figures shown.

1. How many centimeter cubes
   are used in each figure?


2. What pattern do you see? Describe it in words.


3. Suppose this pattern continues. Copy and complete the table to
   find the number of cubes needed to make each figure.
   Figure
   Cubes Needed

1

4

2

8

3

12

45678

4. How many cubes are needed to make the 10th figure? Explain.

A sequence is an ordered list of numbers. Each number in a sequence

is called a term. In an arithmetic sequence, each term is found by

adding the same number to the previous term. An example of an

arithmetic sequence is shown.

8, 11, 14, 17, 20, ...

+ 3 + 3 + 3 + 3

Each term is found by adding

3 to the previous term.

Describe and Extend Sequences

Describe the relationship between the terms in the arithmetic

sequence 8, 13, 18, 23, .... Then write the next three terms in the

sequence.

Each term is found by adding

+ 5 + 5 + 5 5 to the previous term.

8, 13, 18, 23, ...

Continue the pattern to find the next three terms.

23 + 5 = 28 28 + 5 = 33 33 + 5 = 38

The next three terms are 28, 33, and 38.

Describe the relationship between the terms in each arithmetic

sequence. Then write the next three terms in the sequence.

a. 0, 13, 26, 39, ... b. 4, 7, 10, 13 ...

Main Idea

Describe the

relationships and

extend terms in

arithmetic sequences.

Vocabulary

sequence

term

arithmetic sequence

geometric sequence

V Figure 1 Figure 2 Figure 3

s

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