Series and Sequences Practice Test

[Pages:4]Algebra 2

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Series and Sequences Practice Test

Date________________ Period____

Find the first four terms in each sequence.

1) a = n2 + 3 n

2n + 1 2) a =

n 2n

3) a = a ? -6

n

n - 1

a = -2 1

Evaluate each series.

7

S 5) (20 - k) k = 1

2 + a

4) a =

n - 1

n

2

a = -30 1

25

S 6) m2 m = 1

13

S 7) a a = 1

7

S 8) (2k2 - 2) k = 1

Determine if the sequence is arithmetic. If it is, find the common difference and the 52nd term.

9) -9, -16, -23, -30, ...

10) 30, 35, 40, 45, ...

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

11) a = -1038 and a = -3738

11

38

Find a 35

12) a = 27 and a = 111

10

31

Find a 38

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Evaluate each arithmetic series described. 13) 6 + 12 + 18 + 24..., n = 12

13

S 15) (3n - 4) n = 1

14) 16 + 19 + 22 + 25..., n = 15

40

S 16) (5n + 1) n = 1

Determine if the sequence is geometric. If it is, find the common ratio and the term named in the problem.

17) 2, 4, 8, 16, ... Find a

9

18) -4, 12, -36, 108, ... Find a

12

Given two terms in a geometric sequence find the term named in the problem.

19) a = 16 and a = 1024

2

5

Find a 9

20) a = 243 and a = 81

5

4

Find a 9

Evaluate each geometric series described. 21) 108 + 36 + 12 + 4..., n = 7

22) -1 - 3 - 9 - 27..., n = 8

S ( )9 1 i - 1

23) i=1 2

10

S 24) -2 ? 2n - 1 n = 1

Determine if the series converges or diverges. If it converges, evaluate the series described.

?

S 25) 4k - 1 k = 1

?

S 26) 2.7 ? 0.6m - 1 m = 1

S ( )? 4 k - 1

27) k=1 5

?

S 28) 1.8 ? 0.4m - 1 m = 1

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Worksheet by Kuta Software LLC

Algebra 2

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Series and Sequences Practice Test

Date________________ Period____

Find the first four terms in each sequence.

1) a = n2 + 3 n 4, 7, 12, 19

3) a = a ? -6

n

n - 1

a = -2 1

-2, 12, -72, 432

2n + 1 2) a =

n 2n

3579 , , ,

2468

2 + a

4) a =

n - 1

n

2

a = -30 1

-30, -14, -6, -2

Evaluate each series.

7

S 5) (20 - k) k = 1

112

25

S 6) m2 m = 1

5525

13

S 7) a a = 1

91

7

S 8) (2k2 - 2) k = 1

266

Determine if the sequence is arithmetic. If it is, find the common difference and the 52nd term.

9) -9, -16, -23, -30, ...

10) 30, 35, 40, 45, ...

Common Difference: d = -7 a = -366

52

Common Difference: d = 5 a = 285

52

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

11) a = -1038 and a = -3738

11

38

Find a 35

Common Difference: d = -100 a = -3438

35

12) a = 27 and a = 111

10

31

Find a 38

Common Difference: d = 4 a = 139

38

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Worksheet by Kuta Software LLC

Evaluate each arithmetic series described. 13) 6 + 12 + 18 + 24..., n = 12

468

13

S 15) (3n - 4) n = 1 221

14) 16 + 19 + 22 + 25..., n = 15 555

40

S 16) (5n + 1) n = 1 4140

Determine if the sequence is geometric. If it is, find the common ratio and the term named in the problem.

17) 2, 4, 8, 16, ...

18) -4, 12, -36, 108, ...

Find a 9

Find a 12

Common Ratio: r = 2

Common Ratio: r = -3

a = 512 9

a = 708588 12

Given two terms in a geometric sequence find the term named in the problem.

19) a = 16 and a = 1024

2

5

Find a 9

a = 262144 9

20) a = 243 and a = 81

5

4

Find a 9

a = 19683 9

Evaluate each geometric series described. 21) 108 + 36 + 12 + 4..., n = 7

4372 27

22) -1 - 3 - 9 - 27..., n = 8 -3280

S ( )9 1 i - 1

23) i=1 2

511 256

10

S 24) -2 ? 2n - 1 n = 1

-2046

Determine if the series converges or diverges. If it converges, evaluate the series described.

?

S 25) 4k - 1 k = 1

No sum

?

S 26) 2.7 ? 0.6m - 1 m = 1

6.75

S ( )? 4 k - 1

27) k=1 5

?

S 28) 1.8 ? 0.4m - 1 m = 1

5

3

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Worksheet by Kuta Software LLC

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