Page 226 - Algebra 1

L E S S O N Recognizing and Extending Arithmetic
34
Sequences
Warm Up
New Concepts
1. Vocabulary Any quantity whose value does not change is called
(2)
Simplify.
2. 7.2 - 5.8 - (-15)
(6)
4. 6(-2.5) (11)
a.
3. -0.12 - (-43.7) - 73.5 (6)
5. (-15) (-4.2) (11)
Math Language
The symbol “...” is an ellipsis and is read “and so on.” In mathematics, the symbol means
the pattern continues without end.
Example
1
Online Connection www.SaxonMathResources.com
Sequences of numbers can be formed using a variety of patterns and operations. A sequence is a list of numbers that follow a rule, and each number in the sequence is called a term of the sequence. Here are a few examples of sequences:
1, 3, 5, 7, ... 7, 4, 1, -2, ... 2, 6, 18, 54, ... 1, 4, 9, 16, ...
In the above examples, the first two sequences are a special type of sequence called an arithmetic sequence. An arithmetic sequence is a sequence that has a constant difference between two consecutive terms called the common difference.
To find the common difference, choose any term and subtract the previous term. In the first sequence above, the common difference is 2, while in the second sequence, the common difference is -3.
1, 3, 5, 7, ... 7, 4, 1, -2, ...
+2 +2 +2 -3 -3 -3
If the sequence does not have a common difference, then it is not arithmetic.
Recognizing Arithmetic Sequences
Determine if each sequence is an arithmetic sequence. If yes, find the common difference and the next two terms.
a. 7, 12, 17, 22, ...
SOLUTION Since12-7=5,17-12=5,and22-17=5,thesequenceis arithmetic with a common difference of 5. The next two terms are 22 + 5 = 27 and 27 + 5 = 32.
b. 3, 6, 12, 24, ...
SOLUTION Since 6 - 3 = 3 and 12 - 6 = 6, there is no common difference
and the sequence is not arithmetic.
Lesson 34 211