Algebra 1 Name_________________________Date____Section___________________________________
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Worksheet
Determine if the sequence is arithmetic. If it is, find the common difference, the nth term, and
the term named in the problem
1) 1, 11, 21, 31, ...
Find a34
2) -11, 189, 389, 589, ...
Find a33
3) -33, 67, 167, 267, ...
Find a33
4) 3, -7, -17, -27, ...
Find a22
Given the first term and the common difference of an arithmetic sequence find the nth term and
the term named in the problem
5) a1 = -30, d = 3
Find a23
6) a1 = -9, d = 100
Find a27
7) a1 = 13, d = 8
Find a30
8) a1 = 35, d = 6
Find a40
Given a term in an arithmetic sequence and the common difference find the first term, the nth
term, and theterm named in the problem
9) a28 = 174, d = 5
Find a38
10) a32 = -6212, d = -200
Find a25
Worksheet by Kuta Software LLC
-1-
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11) a25 = 754, d = 30
Find a34
12) a36 = 7039, d = 200
Find a33
13) a13 = 111, d = 10
Find a22
Given the a random term and the first term of an arithmetic sequence, find the common
difference
14) a1= 5 and a20=100
15) a1=-8 and a31=116
16) a1=7 and a25=-137
17) a1=12 and a21=172
For each sequence, determine if it is arithmetic and justify why. Then, answer the given
question
18) 17, 25, 33, 41
what term is 225?
19) -19, -24, -29, -34
what term is -184
20) -31, -27, -23, -19
what term is 77
21) -15, -22, -29, -36
what term is -372
Worksheet by Kuta Software LLC
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Answers to Worksheet
1) Common Difference: d = 10
a34 = 331
Explicit: an = -9 + 10n
3) Common Difference: d = 100
a33 = 3167
Explicit: an = -133 + 100n
5) a23 = 36
Explicit: an = -33 + 3n
8) a40 = 269
Explicit: an = 29 + 6n
10)
11)
13)
16)
18)
19)
20)
21)
2) Common Difference: d = 200
a33 = 6389
Explicit: an = -211 + 200n
4) Common Difference: d = -10
a22 = -207
Explicit: an = 13 - 10n
6) a27 = 2591
7) a30 = 245
Explicit: an = -109 + 100n
Explicit: an = 5 + 8n
9) First Five Terms: 39, 44, 49, 54, 59
a38 = 224
Explicit: an = 34 + 5n
First Five Terms: -12, -212, -412, -612, -812
a25 = -4812
Explicit: an = 188 - 200n
First Five Terms: 34, 64, 94, 124, 154
12) First Five Terms: 39, 239, 439, 639, 839
a34 = 1024
a33 = 6439
Explicit: an = 4 + 30n
Explicit: an = -161 + 200n
14) 5
15) 4
First Five Terms: -9, 1, 11, 21, 31
a22 = 201
Explicit: an = -19 + 10n
-6
17) 8
It is arithmetic because the commond difference is constant; d=8
the term number is 27; that is a27=225
It is arithmetic because the commond difference is constant; d=-5
the term number is 34; that is a34=-184
It is arithmetic because the commond difference is constant; d=4
the term number is 28; that is a28=77
It is arithmetic because the commond difference is constant; d=-7
the term number is 52; that is a52=-372
Worksheet by Kuta Software LLC
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