Name: ___________________________________
Unit 10: Sequences & Series
Date: ________________________ Bell: ______
Homework 2: Arithmetic Sequences and Series
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Directions: Determine whether the sequence is arithmetic. If yes, identify the common difference
and give the next three terms.
1. {−3, − 12, − 48, − 192, ... }
2. {−18, − 27, − 36, − 45, ... }
3. {4, 11, 18, 25, ... }
4. {16, 8, 4, 1, ... }
5. {−9, − 33, − 57, − 81, ... }
1 5 7 3
6.  , , , , ... 
2 6 6 2

Directions: Write a rule for each sequence, then find the indicated term.
7. {12, 27, 42, 57, ... } ; a18
8. {29, 9, − 11, − 31, ... } ; a32
9. {−40, − 44, − 48, − 52, ... } ; a49
10. {50, 39, 28, 17, ... } ; a54
11. Karen’s New Year’s resolution is to work out each day on her ellipitcal. The number of calories
she has burned each day since she started is shown below. Write a rule for the sequence, and
find the number of calories that Karen will burn on the 30th day.
{349, 357, 365, 373, 381, ... }
© Gina Wilson (All Things Algebra), 201
Directions: If the given terms are part of an arithmetic sequence, write a rule for the sequence,
then find a9
12. a1 = 11 and a5 = 27
13. a1 = 3 and a14 = −23
14. a1 = −5 and a7 = 91
15. a1 =
1
and a23 = 6
2
Directions: Find the indicated sum for each arithmetic series.
16. {4 + 6 + 8 + 10 + ...} ; S21
17. {24 + 31 + 38 + 45 + ...} ; S 9
18. {15 + 4 + ( −7) + ( −18) + ...} ; S12
19.
25
∑ ( 5k + 1)
k =1
20.
14
∑ (17 − 6n )
n=9
21.
35
∑ ( 3x − 12)
x = 11
© Gina Wilson (All Things Algebra), 201