Sequences/Series Test Practice Date Period

ID: 1

Algebra 2

Name___________________________________

Sequences/Series Test Practice

Date________________ Period____

If the sequence is arithmetic or geometric, find the next 3 terms.

5

5

5

5

, ...

1) ?5, ? , ? , ? , ?

4

16

64

256

2) 1, 3, 6, 10, 15, ...

3) ?11, 89, 189, 289, 389, ...

4) ?38, ?36, ?34, ?32, ?30, ...

Given the first term and the common difference of an arithmetic sequence find the term named in the

problem.

5) a1 = ?9, d = 2

6) a1 = ?14, d = ?10

Find a20

Find a38

Find the missing term or terms in each arithmetic sequence.

7) ..., ?20, ___, ___, ___, 0, ...

8) ..., 26, ___, ___, ___, ___, 41, ...

Given the first term and the common ratio of a geometric sequence find the term named in the problem.

9) a1 = ?4, r = ?2

10) a1 = 2, r = ?2

Find a10

Find a11

Find the missing term or terms in each geometric sequence.

11) ..., ?1, ___, ___, ___, ?256, ...

12) ..., ?2, ___, ___, ___, ___, ?2048, ...

Evaluate each arithmetic series described.

8

13)

¦² (2k + 7)

10

14)

k=2

¦² (5 ? 3i)

i=3

15) a1 = 16, d = 3, n = 5

16) a1 = 7, d = 7, n = 45

17) 6 + 8 + 10 + 12..., n = 7

18) (?2) + 2 + 6 + 10..., n = 19

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Worksheet by Kuta Software LLC

Determine the number of terms n in each arithmetic series.

19) a1 = 26, an = 166, S n = 1440

20) a1 = 10, an = 451, S n = 11525

Evaluate each geometric series described.

21) ?3 + 15 ? 75 + 375..., n = 6

9

23)

¦²

i=1

()

1

?2 ?

5

22) 1 + 5 + 25 + 125..., n = 8

7

i?1

24)

¦² 2 ? (?6)

i?1

i=1

Evaluate each infinite geometric series described.

¡Þ

( )

4

25)

108 ? ?

3

m=1

¦²

27) 6 ?

m?1

3 3

3

+ ? ...

2 8 32

¡Þ

()

1

26)

?2 ?

2

n=1

¦²

28) 2 ?

n?1

2 2

2

+ ? ...

3 9 27

Determine the number of terms n in each geometric series.

29) a1 = ?2, r = ?6, S n = 13330

30) a1 = ?3, r = ?6, S n = 555

Given the recursive formula for an arithmetic sequence find the first five terms.

31) an + 1 = an + n

32) an + 1 = an ? an + 1

a1 = 7

a1 = 2

a2 = 3

33) an + 1 = an + n

34) an + 1 = an + n

a1 = 3

a1 = ?10

35) an + 1 = an + n

36) an + 1 = an + 9

a1 = ?9

a1 = ?13

37) an + 1 = an ? 4

38) an + 1 = an ? ?5

a1 = ?2

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a1 = 3

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Worksheet by Kuta Software LLC

Answers to Sequences/Series Test Practice (ID: 1)

2) 21, 28, 36

5

5

5

, ?

, ?

1024

4096

16384

4) ?28, ?26, ?24

5) a20 = 29

3) 489, 589, 689

6) a38 = ?384

8) 29, 32, 35, 38

10) a11 = 2048

1) ?

11)

14)

18)

22)

26)

30)

34)

37)

9) a10 = 2048

7) ?15, ?10, ?5

?4, ?16, ?64 or 4, -16, 64

12) ?8, ?32, ?128, ?512

13) 119

?116

15) 110

16) 7245

17) 84

646

19) 15

20) 50

21) 7812

25) No sum

97656

24) 79982

976562

23) ?

390625

?4

29) 6

24

3

27)

28)

5

2

32) 2, 3, -1, 4, -5

4

31) 7, 12, 17, 22, 27

33) 3, 5, 8, 12

?10, ?8, ?5, ?1

35) ?9, ?7, ?4, 0

36) ?13, ?4, 5, 14

?2, ?8, ?32, ?128, ?512

38) 3, ?15, 75, ?375, 1875

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Worksheet by Kuta Software LLC

ID: 2

Algebra 2

Name___________________________________

Sequences/Series Test Practice

Date________________ Period____

If the sequence is arithmetic or geometric, find the next 3 terms.

1) 4, ?8, 16, ?32, 64, ...

3) 3, 15, 75, 375, 1875, ...

5 7 9 11

, ,

,

, ...

4 9 16 25

2) 3,

4) 1, 4, 9, 16, 25, ...

Given the first term and the common difference of an arithmetic sequence find the term named in the

problem.

5) a1 = 6, d = 2

6) a1 = ?39, d = ?3

Find a22

Find a39

Find the missing term or terms in each arithmetic sequence.

7) ..., 32, ___, ___, ___, 8, ...

8) ..., 1, ___, ___, ___, ___, 501, ...

Given the first term and the common ratio of a geometric sequence find the term named in the problem.

9) a1 = ?1, r = ?2

10) a1 = ?4, r = 3

Find a11

Find a11

Find the missing term or terms in each geometric sequence.

11) ..., 2, ___, ___, ___, ___, 15552, ...

12) ..., 3, ___, ___, ___, ___, 9375, ...

Evaluate each arithmetic series described.

10

13)

¦² (7k ? 12)

10

14)

k=3

¦² (8m ? 5)

m=5

15) a1 = ?10, d = ?10, n = 13

16) a1 = 6, d = ?2, n = 9

17) (?4) + (?2) + 0 + 2..., n = 8

18) 17 + 20 + 23 + 26..., n = 7

Determine the number of terms n in each arithmetic series.

19) a1 = 5, an = 65, S n = 455

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20) a1 = 15, an = 35, S n = 150

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Worksheet by Kuta Software LLC

Evaluate each geometric series described.

21) ?4 ? 24 ? 144 ? 864..., n = 6

22) ?

9

23)

¦²

1 1

1

1

+ ?

+ ..., n = 7

4 8 16 32

8

4

n?1

24)

n=1

¦²5

m?1

m=1

Evaluate each infinite geometric series described.

¡Þ

25)

¦²

m=1

27) 3 +

()

27 4

?

32 3

m?1

3

3

3

+

+ ...

4 16 64

¡Þ

26)

¦²

n=1

?

()

27 2

?

2

3

n?1

28) ?1.3 ? 1.04 ? 0.832 ? 0.6656...

Determine the number of terms n in each geometric series.

29) a1 = ?4, r = ?6, S n = ?124

30) a1 = ?1, r = 2, S n = ?7

Given the recursive formula for an arithmetic sequence find the first five terms.

31) an + 1 = an ? 7

32) an + 1 = an ? 2

a1 = ?40

a1 = 30

33) an + 1 =

2 + an

34) an + 1 = an + n

2

a1 = ?6

a1 = ?22

35) an + 1 = an ? 2

36) an + 1 = nan

a1 = 1

37) an + 1 = an ? ?4

a1 = ?1

38) an + 1 = an ? ?5

a1 = 1

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a1 = ?3

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Worksheet by Kuta Software LLC

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