Arithmetic Sequences Date Period
Kuta Software - Infinite Algebra 2
Name___________________________________
Arithmetic Sequences
Date________________ Period____
Determine if the sequence is arithmetic. If it is, find the common difference.
1) 35, 32, 29, 26, ...
2) ?3, ?23, ?43, ?63, ...
3) ?34, ?64, ?94, ?124, ...
4) ?30, ?40, ?50, ?60, ...
5) ?7, ?9, ?11, ?13, ...
6) 9, 14, 19, 24, ...
Given the explicit formula for an arithmetic sequence find the first five terms and the term named in the
problem.
7) an = ?11 + 7n
Find a34
8) an = 65 ? 100n
Find a39
9) an = ?7.1 ? 2.1n
Find a27
10) an =
11 1
+ n
8
2
Find a23
Given the first term and the common difference of an arithmetic sequence find the first five terms and the
explicit formula.
11) a1 = 28, d = 10
12) a1 = ?38, d = ?100
13) a1 = ?34, d = ?10
14) a1 = 35, d = 4
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-1-
Worksheet by Kuta Software LLC
Given a term in an arithmetic sequence and the common difference find the first five terms and the
explicit formula.
15) a38 = ?53.2, d = ?1.1
16) a40 = ?1191, d = ?30
17) a37 = 249, d = 8
18) a36 = ?276, d = ?7
Given the first term and the common difference of an arithmetic sequence find the recursive formula and
the three terms in the sequence after the last one given.
3
1
19) a1 = , d = ?
5
3
20) a1 = 39, d = ?5
21) a1 = ?26, d = 200
22) a1 = ?9.2, d = 0.9
Given a term in an arithmetic sequence and the common difference find the recursive formula and the
three terms in the sequence after the last one given.
23) a21 = ?1.4, d = 0.6
24) a22 = ?44, d = ?2
25) a18 = 27.4, d = 1.1
26) a12 = 28.6, d = 1.8
Given two terms in an arithmetic sequence find the recursive formula.
27) a18 = 3362 and a38 = 7362
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28) a18 = 44.3 and a33 = 84.8
-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
Arithmetic Sequences
Date________________ Period____
Determine if the sequence is arithmetic. If it is, find the common difference.
1) 35, 32, 29, 26, ...
2) ?3, ?23, ?43, ?63, ...
d = ?3
3) ?34, ?64, ?94, ?124, ...
d = ?20
4) ?30, ?40, ?50, ?60, ...
d = ?30
5) ?7, ?9, ?11, ?13, ...
d = ?10
6) 9, 14, 19, 24, ...
d = ?2
d =5
Given the explicit formula for an arithmetic sequence find the first five terms and the term named in the
problem.
7) an = ?11 + 7n
Find a34
8) an = 65 ? 100n
Find a39
First Five Terms: ?35, ?135, ?235, ?335, ?435
a39 = ?3835
First Five Terms: ?4, 3, 10, 17, 24
a34 = 227
9) an = ?7.1 ? 2.1n
Find a27
11 1
15 19 23 27 31
+ n First Five Terms: ,
,
,
,
8
2
8 8 8 8 8
Find a23
103
a23 =
First Five Terms: ?9.2, ?11.3, ?13.4, ?15.5, ?17.6
8
a27 = ?63.8
10) an =
Given the first term and the common difference of an arithmetic sequence find the first five terms and the
explicit formula.
11) a1 = 28, d = 10
12) a1 = ?38, d = ?100
First Five Terms: ?38, ?138, ?238, ?338, ?438
Explicit: an = 62 ? 100n
First Five Terms: 28, 38, 48, 58, 68
Explicit: an = 18 + 10n
13) a1 = ?34, d = ?10
14) a1 = 35, d = 4
First Five Terms: ?34, ?44, ?54, ?64, ?74
Explicit: an = ?24 ? 10n
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First Five Terms: 35, 39, 43, 47, 51
Explicit: an = 31 + 4n
-1-
Worksheet by Kuta Software LLC
Given a term in an arithmetic sequence and the common difference find the first five terms and the
explicit formula.
15) a38 = ?53.2, d = ?1.1
16) a40 = ?1191, d = ?30
First Five Terms: ?12.5, ?13.6, ?14.7, ?15.8, ?16.9 First Five Terms: ?21, ?51, ?81, ?111, ?141
Explicit: an = ?11.4 ? 1.1n
Explicit: an = 9 ? 30n
17) a37 = 249, d = 8
18) a36 = ?276, d = ?7
First Five Terms: ?39, ?31, ?23, ?15, ?7
Explicit: an = ?47 + 8n
First Five Terms: ?31, ?38, ?45, ?52, ?59
Explicit: an = ?24 ? 7n
Given the first term and the common difference of an arithmetic sequence find the recursive formula and
the three terms in the sequence after the last one given.
3
1
4
1
2
19) a1 = , d = ?
Next 3 terms: , ? , ?
5
3
15
15
5
1
Recursive: an = an ? 1 ?
3
3
a1 =
5
20) a1 = 39, d = ?5
21) a1 = ?26, d = 200
22) a1 = ?9.2, d = 0.9
Next 3 terms: 34, 29, 24
Recursive: an = an ? 1 ? 5
a1 = 39
Next 3 terms: 174, 374, 574
Recursive: an = an ? 1 + 200
Next 3 terms: ?8.3, ?7.4, ?6.5
Recursive: an = an ? 1 + 0.9
a1 = ?26
a1 = ?9.2
Given a term in an arithmetic sequence and the common difference find the recursive formula and the
three terms in the sequence after the last one given.
23) a21 = ?1.4, d = 0.6
24) a22 = ?44, d = ?2
Next 3 terms: ?0.8, ?0.2, 0.4
Recursive: an = an ? 1 + 0.6
a1 = ?13.4
25) a18 = 27.4, d = 1.1
Next 3 terms: ?46, ?48, ?50
Recursive: an = an ? 1 ? 2
a1 = ?2
26) a12 = 28.6, d = 1.8
Next 3 terms: 28.5, 29.6, 30.7
Recursive: an = an ? 1 + 1.1
a1 = 8.7
Next 3 terms: 30.4, 32.2, 34
Recursive: an = an ? 1 + 1.8
a1 = 8.8
Given two terms in an arithmetic sequence find the recursive formula.
27) a18 = 3362 and a38 = 7362
28) a18 = 44.3 and a33 = 84.8
an = an ? 1 + 200
a1 = ?38
an = an ? 1 + 2.7
a1 = ?1.6
Create your own worksheets like this one with Infinite Algebra 2. Free trial available at
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-2-
Worksheet by Kuta Software LLC
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