7th Grade Math

Lesson 2B Patterns 45

Arithmetic sequences can also involve decimals.

Describe and Extend Sequences

Describe the relationship between the terms in the arithmetic

sequence 0.4, 0.6, 0.8, 1.0,.... Then write the next three terms in

the sequence.

Each term is found by adding

+0.2 0.2 to the previous term.

0.4, 0.6, 0.8, 1.0, ...

+0.2+0.2

Continue the pattern to find the next three terms.

1.0 + 0.2 = 1.2 1.2 + 0.2 = 1.4 1.4 + 0.2 = 1.6

The next three terms are 1.2, 1.4, and 1.6.

Describe the relationship between the terms in each arithmetic

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

c. 1.0, 1.3, 1.6, 1.9, ... d. 2.5, 3.0, 3.5, 4.0, ...

e. 1.75, 2.5, 3.25, 4.0 ... f. 0.01, 0.02, 0.03, 0.04 ...

In a sequence, each term has a specific position within the

sequence. Consider the sequence 2, 4, 6, 8, 10, ....

,, ,, ,, ,, ,...,

1st position

2nd position 4th position

3rd position 5th position

The table below shows the position of each term in this sequence.

Notice that as the position number increases by 1, the value of the

term increases by 2.

Position Operation Value of Term

11 · 2 = 22

22 · 2 = 44

33 · 2 = 66

44 · 2 = 88

55 · 2 = 10 10

+ 2

+ 2

+ 2

+ 2

+ 1

+ 1

+ 1

+ 1

You can also write an algebraic expression to represent the

relationship between any term in a sequence and its position in the

sequence. In this case, if n represents the position in the sequence, the

value of the term is 2n.

seque

Arithmetic Sequences Arithmetic Sequences

When looking for a pattern

between the position

number and each term in

the sequence, it is often

helpful to make a table.

044_050_C1_L2_895130.indd 45 12/29/09 12:22 PM