Name ________________________________________ Date __________________ Class ______________
Constructing Arithmetic Sequences
LESSON
4-2
Practice and Problem Solving: A/B
Write an explicit rule and a recursive rule using the table.
1.
n
1
2
3
4
5
an
8
12
16
20
24
2.
n
1
2
3
4
5
an
11
7
3
-1
-5
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3.
n
1
2
3
4
5
an
-20
-13
-6
1
8
4.
n
1
2
3
4
5
an
2.7
4.3
5.9
7.5
9.1
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Write an explicit rule and a recursive rule using the sequence.
5. 45, 50, 55, 60, 65
6. 94, 87, 80, 73, 66
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8. 83, 43, 3, -37, -77
7. 12, 26, 40, 54, 68
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Solve.
9. The explicit rule for an arithmetic sequence is an = 7 + 6n.
Find the first four terms of the sequence.
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10. Helene paid back $100 in Month 1 of her loan. In each month after that,
Helene paid back $50. The graph shows the sequence. Write an explicit
rule to represent the situation.
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Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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Name ________________________________________ Date __________________ Class ______________
LESSON 4-2
Practice and Problem Solving: A/B
Explicit Rule: 𝑎" = 4𝑛 + 4
1.
Recursive Rule: 𝑎" = 𝑎"'( + 4, 𝑎( = 8
Explicit Rule: 𝑎" = −4𝑛 + 15
2.
Recursive Rule: 𝑎" = 𝑎"'( − 4, 𝑎( = 11
3. Explicit Rule: 𝑎" = 7𝑛 − 27
Recursive Rule: 𝑎" = 𝑎"'( + 7, 𝑎( = −20
4. Explicit Rule: 𝑎" = 1.6𝑛 + 1.1
Recursive Rule: 𝑎" = 𝑎"'( + 1.6, 𝑎( = 2.7
5. Explicit Rule: 𝑎" = 5𝑛 + 40
Recursive Rule: 𝑎" = 𝑎"'( + 5, 𝑎( = 45
6. Explicit Rule: 𝑎" = −7𝑛 + 101
Recursive Rule: 𝑎" = 𝑎"'( − 7, 𝑎( = 94
Explicit Rule: 𝑎" = 14𝑛 − 2
7.
Recursive Rule: 𝑎" = 𝑎"'( + 14, 𝑎( = 12
Explicit Rule: 𝑎" = −40𝑛 + 123
8.
Recursive Rule: 𝑎" = 𝑎"'( − 40, 𝑎( = 83
9.
13, 19, 25, 31
10.
f(n) = 50 + 50n
or 𝑎" = 50𝑛 + 50
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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