• sequence
• term
• finite sequence
• infinite sequence
• arithmetic sequence
• common difference
• geometric sequence
• common ratio
Identify Arithmetic Sequences
A. Determine whether the sequence is arithmetic.
–3, –8, –13, –23, …
–3
–8
–5
–13
–5
–23
–10
There is no common difference.
Answer: This is not an arithmetic sequence.
Identify Arithmetic Sequences
B. Determine whether the sequence is arithmetic.
–8, –2, 4, 10, …
–8
–2
+6
4
+6
10
+6
The common difference is 6.
Answer: The sequence is arithmetic.
A. Determine whether the sequence is arithmetic.
If so, determine the common difference.
–16, –5, 6, 17, …
A. The common difference is 9.
A
D. The sequence is not arithmetic.
0%
B
0%
A
B
C
0%
D
D
C. The common difference is 13.
A.
B.
C.
0%
D.
C
B. The common difference is 11.
B. Determine whether the sequence is arithmetic.
If so, determine the common difference.
22, 14, 6, 2, …
A. The common difference is –8.
A
D. The sequence is not arithmetic.
0%
B
0%
A
B
C
0%
D
D
C. The common difference is 8.
A.
B.
C.
0%
D.
C
B. The common difference is 5.
Graph an Arithmetic Sequence
A. Consider the arithmetic sequence –8, –6, –4, ….
Find the next four terms of the sequence.
Step 1 To determine the common difference, subtract
any term from the term directly after it. The
common difference is –4, – (–6) or 2.
Step 2 To find the next term, add 2 to the last term.
Continue to add 2 to find the following terms.
–8
–6
+2
–4
+2
+2
–2
+2
0
2
+2
4
+2
Answer: The next four terms are –2, 0, 2, and 4.
A. Consider the arithmetic sequence
22, 13, 4, … . Find the next four terms of the
sequence.
A. 4, 8, 12, and 16
A
0%
0%
B
D. 5, 14, 23, and 32
A
B
C
0%
D
D
C. 3, 12, 21, and 30
A.
B.
C.
0%
D.
C
B. 6, 15, 24, and 33
Graph an Arithmetic Sequence
B. Consider the arithmetic sequence –8, –6, –4, ….
Graph the first seven terms of the sequence.
The domain contains the terms {1, 2, 3, 4, 5, 6, 7} and
the range contains the terms {–8, –6, –4, –2, 0, 2, 4}.
So, graph the corresponding pairs.
Answer:
B. Consider the arithmetic sequence
22, 13, 4, … . Graph the first seven terms of the
sequence.
0%
A
B
C
0%
D
D
0%
A.
B.
C.
0%
D.
C
D.
B
C.
B.
A
A.
Identify Geometric Sequences
A. Determine whether the sequence is geometric.
8, 20, 50, 125, …
Find the ratios of the consecutive terms.
Answer: The ratios are the same, so the sequence is
geometric.
Identify Geometric Sequences
B. Determine whether the sequence is geometric.
19, 30, 41, 52, …
Answer: The ratios are not the same, so the
sequence is not geometric.
A. Determine whether the sequence is geometric.
–4, 8, –16, 32, …
A. The sequence is geometric.
B. The sequence is not geometric.
1.
2.
A. A
B. B
A
B
Graph a Geometric Sequence
A. Consider the geometric sequence
10, 15, 22.5, … .
Find the next three terms of the sequence.
Step 1 Find the value of the common ratio:
Step 2 To find the next term, multiply the previous
term by
Continue multiplying by
following terms.
to find the
Graph a Geometric Sequence
10
15
22.5
33.75
50.625
75.938
Answer: The next three terms are 33.75, 50.625, and
75.938.
Graph a Geometric Sequence
B. Graph the first six terms of the sequence.
Domain: {1, 2, 3, 4, 5, and 6}
Range: {10, 15, 22.5, 33.75, 50.625, 75.938}
Answer:
A. Consider the geometric sequence 2, 6, 18, … .
Find the next three terms of the sequence.
A. 30, 42, 54
B. 36, 72, 144
0%
B
A
0%
A
B
C
0%
D
D
D. 54, 162, 486
C
C. 72, 288, 1152
A.
B.
C.
0%
D.
B. Graph the first six terms of the sequence.
0%
A
B
C
0%
D
D
0%
A.
B.
C.
0%
D.
C
D.
B
C.
B.
A
A.
Classify Sequences
B. Determine whether the sequence is arithmetic,
geometric, or neither. Explain your reasoning.
2, 5, 9, 14, …
Check for a common difference.
14 – 9 = 5
9–5=4 
Check for a common ratio.

Answer: Because there is no common difference or
common ratio, the sequence is neither
arithmetic nor geometric.
A. Determine whether the sequence is arithmetic,
geometric, or neither. Explain your reasoning.
8, 24, 48, 96, …
A. The sequence is arithmetic.
B. The sequence is geometric.
C. The sequence is neither.
1.
2.
3.
A
B
C