Arithmetic and Geometric Sequences Practice

PreCalculus

Name___________________________________ ID: 1

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Arithmetic and Geometric Sequences Practice

Date________________ Period____

Find the common difference, the term named in the problem, the explicit formula, and the three terms in the sequence after the last one given.

1) -32, 168, 368, 568, ... Find a

20

2) 3, -2, -7, -12, ... Find a

36

Given the second term and the common difference of an arithmetic sequence find the term named in the problem and the explicit formula.

3) a = 16, d = -9 2 Find a 21

4) a = 45, d = 7 2 Find a 28

Given a term in an arithmetic sequence and the common difference find the term named in the problem and the explicit formula.

5) a = 38, d = 2 24 Find a 36

6) a = -60, d = -10 9 Find a 35

Given two terms in an arithmetic sequence find the common difference, the term named in the problem, and the explicit formula.

7) a = -73 and a = -280

12

35

Find a 28

8) a = -1268 and a = -3468

14

36

Find a 30

Worksheet by Kuta Software LLC

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Find the common ratio, the term named in the problem, the explicit formula, and the three terms in the sequence after the last one given.

9) -4, -8, -16, -32, ... Find a

11

10) -1, 2, -4, 8, ... Find a

12

Given the first term and the common ratio of a geometric sequence find the term named in the problem, the explicit formula, and the three terms in the sequence after the last one given.

11) a = 1, r = 3 1 Find a 9

12) a = -4, r = 3 1 Find a 12

Given a term in a geometric sequence and the common ratio find the term named in the problem, the explicit formula, and the three terms in the sequence after the last one given.

13) a = 12, r = -3 2 Find a 9

14) a = -64, r = -2 5 Find a 10

Given two terms in a geometric sequence find the common ratio, the term named in the problem, and the explicit formula.

15) a = -972 and a = -36

6

3

Find a 12

16) a = 128 and a = 64

6

5

Find a 12

Worksheet by Kuta Software LLC

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PreCalculus

Name___________________________________ ID: 1

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Arithmetic and Geometric Sequences Practice

Date________________ Period____

Find the common difference, the term named in the problem, the explicit formula, and the three terms in the sequence after the last one given.

1) -32, 168, 368, 568, ... Find a

20

Common Difference: d = 200 Next 3 terms: 768, 968, 1168 a = 3768

20

Explicit: a = -232 + 200n n

2) 3, -2, -7, -12, ... Find a

36

Common Difference: d = -5 Next 3 terms: -17, -22, -27 a = -172

36

Explicit: a = 8 - 5n n

Given the second term and the common difference of an arithmetic sequence find the term named in the problem and the explicit formula.

3) a = 16, d = -9 2 Find a 21

a = -155 21

Explicit: a = 34 - 9n n

4) a = 45, d = 7 2 Find a 28

a = 227 28

Explicit: a = 31 + 7n n

Given a term in an arithmetic sequence and the common difference find the term named in the problem and the explicit formula.

5) a = 38, d = 2 24 Find a 36

a = 62 36

Explicit: a = -10 + 2n n

6) a = -60, d = -10 9 Find a 35

a = -320 35

Explicit: a = 30 - 10n n

Given two terms in an arithmetic sequence find the common difference, the term named in the problem, and the explicit formula.

7) a = -73 and a = -280

12

35

Find a 28

Common Difference: d = -9 a = -217

28

Explicit: a = 35 - 9n n

8) a = -1268 and a = -3468

14

36

Find a 30

Common Difference: d = -100 a = -2868

30

Explicit: a = 132 - 100n n

Worksheet by Kuta Software LLC

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Find the common ratio, the term named in the problem, the explicit formula, and the three terms in the sequence after the last one given.

9) -4, -8, -16, -32, ... Find a

11

Common Ratio: r = 2 Next 3 terms: -64, -128, -256 a = -4096

11

Explicit: a = -4 ? 2 n - 1 n

10) -1, 2, -4, 8, ... Find a

12

Common Ratio: r = -2 Next 3 terms: -16, 32, -64 a = 2048

12

Explicit: a = -(-2)n - 1 n

Given the first term and the common ratio of a geometric sequence find the term named in the problem, the explicit formula, and the three terms in the sequence after the last one given.

11) a = 1, r = 3 1 Find a 9

Next 3 terms: 3, 9, 27 a = 6561

9

Explicit: a = 3 n - 1 n

12) a = -4, r = 3 1 Find a 12

Next 3 terms: -12, -36, -108 a = -708588

12

Explicit: a = -4 ? 3 n - 1 n

Given a term in a geometric sequence and the common ratio find the term named in the problem, the explicit formula, and the three terms in the sequence after the last one given.

13) a = 12, r = -3 2 Find a 9

Next 3 terms: -36, 108, -324 a = -26244

9

Explicit: a = -4 ? (-3)n - 1 n

14) a = -64, r = -2 5 Find a 10

Next 3 terms: 128, -256, 512 a = 2048

10

Explicit: a = -4 ? (-2)n - 1 n

Given two terms in a geometric sequence find the common ratio, the term named in the problem, and the explicit formula.

15) a = -972 and a = -36

6

3

Find a 12

Common Ratio: r = 3 a = -708588

12

Explicit: a = -4 ? 3 n - 1 n

16) a = 128 and a = 64

6

5

Find a 12

Common Ratio: r = 2 a = 8192

12

Explicit: a = 4 ? 2 n - 1 n

Worksheet by Kuta Software LLC

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