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Name _______________________________________ Date __________________ Class __________________
Review for Mastery
Arithmetic Sequences
An arithmetic sequence is a list of numbers (or terms) with a common difference between
each number. After you find the common difference, you can use it to continue the sequence.
Determine whether each sequence is an arithmetic
sequence. If so, find the common difference and the next three terms.
1,
2,
1
4,
2
8, ...
4
The difference between terms is not constant.
This sequence is not an arithmetic sequence.
0,
6, 12, 18, ...
6
6
6
The difference between terms is constant.
This sequence is an arithmetic sequence with a common difference of 6.
0, 6, 12, 18,
24,
6
30,
6
36
6
Fill in the blanks with the differences between terms. State whether
each sequence is an arithmetic sequence.
1. 14,
12,
10,
8, ...
Is this an arithmetic sequence? _________________
_____ _____ _____
2. 0.3, 0.6, 1.0, 1.5, ...
Is this an arithmetic sequence? _________________
_______ _______ _______
Use the common difference to find the next three terms in each
arithmetic sequence.
3. 7,
4,
1,
2, _____, _____, _____, ...
3 3 3
3
3
3
4. 5,
0,
5,
10, _____, _____, _____, ...
5 5 5
Determine whether each sequence is an arithmetic sequence. If so,
find the common difference and the next three terms.
5. 1, 2, 3, 4, ...
________________________________________________________________________________________
6. 1.25, 3.75, 6.25, 8.75, ...
________________________________________________________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Algebra 1
Name _______________________________________ Date __________________ Class __________________
Review for Mastery
Arithmetic Sequences continued
You can use the first term and common difference of an arithmetic sequence to write a rule in
this form:
an  a1  (n  1)d
any term first term term number common difference
After you write the rule, you can use it to find any term in the sequence.
Find the 50th term of this arithmetic sequence:
5,
3.8,
2.6,
1.4, ...
The first term is 5.
1.2 1.2 1.2
The common difference is 1.2.
First, write the rule.
an  a1  (n  1)d
Write the general form for the rule.
an  5  (n  1)(1.2)
Substitute the first term and common difference.
Now, use the rule to find the 50th term.
a50  5  (50  1)(1.2)
Substitute the term number.
a50  5  (49)(1.2)
Simplify.
a50  5  (58.8)
a50  53.8
The 50th term is 53.8.
Use the first term and common difference to write the rule for each
arithmetic sequence.
7. The arithmetic sequence with first term
a1  10 and common difference d  4.
___________________________
8. 5, 0, 5, 10, ...
first term: a1  ___________________
common difference: d  ___________________
___________________________
Find the indicated term of each arithmetic sequence.
9. an  16  (n  1)(0.5)
15th term: _________________
10. an  6  (n  1)(3)
32nd term: _________________
11. 8, 6, 4, 2, ...
100th term: _________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Algebra 1
Review for Mastery
1. 2, 2, 2; yes
2. 0.3, 0.4, 0.5; no
3. 5, 8, 11
4. 15, 20, 25
5. no
6. yes; 2.5; 11.25, 13.75, 16.25
7. an  10  (n  1)(4)
8. 5; 5; an  5  (n  1)(5)
9. 9
10. 99
11. 190
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Algebra 1