Sequences/Series Test Practice Date Period

[Pages:12]Algebra 2

ID: 1

Name___________________________________

Sequences/Series Test Practice

Date________________ Period____

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

55 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) a = -9, d = 2 1 Find a 20

6) a = -14, d = -10 1 Find a 38

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) a = -4, r = -2 1 Find a 10

10) a = 2, r = -2 1 Find a 11

Find the missing term or terms in each geometric sequence.

11) ..., -1, ___, ___, ___, -256, ...

12) ..., -2, ___, ___, ___, ___, -2048, ...

Evaluate each arithmetic series described.

8

13) (2k + 7)

k = 2

10

14) (5 - 3i)

i = 3

15) a = 16, d = 3, n = 5 1

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

16) a = 7, d = 7, n = 45 1

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

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Determine the number of terms n in each arithmetic series.

19) a = 26, a = 166, S = 1440

1

n

n

20) a = 10, a = 451, S = 11525

1

n

n

Evaluate each geometric series described. 21) -3 + 15 - 75 + 375..., n = 6

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

( ) 9

1 i-1

23) -2

i = 1

5

7

24) 2 (-6)i - 1

i = 1

Evaluate each infinite geometric series described.

( )

4 m-1

25) 108 -

m = 1

3

( )

1 n-1

26) -2

n = 1

2

33 3 27) 6 - + - ...

2 8 32

22 2 28) 2 - + - ...

3 9 27

Determine the number of terms n in each geometric series.

29) a = -2, r = -6, S = 13330

1

n

30) a = -3, r = -6, S = 555

1

n

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

31) a = a + n n+1 n a =7 1

32) a = a - a n+1 n n+1 a =2 1 a =3 2

33) a = a + n n+1 n a =3 1

34) a = a + n n+1 n a = -10 1

35) a = a + n n+1 n a = -9 1

36) a = a + 9 n+1 n a = -13 1

37) a = a 4 n+1 n a = -2 1

38) a = a -5 n+1 n a =3 1

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

5

5

5

1) - , - , -

1024 4096 16384

2) 21, 28, 36

3) 489, 589, 689

4) -28, -26, -24

5) a = 29 20

6) a = -384 38

8) 29, 32, 35, 38

9) a = 2048 10

10) a = 2048 11

11) -4, -16, -64 or 4, -16, 64 12) -8, -32, -128, -512

7) -15, -10, -5 13) 119

14) -116

15) 110

16) 7245

17) 84

18) 646 22) 97656

19) 15 976562

23) - 390625

20) 50 24) 79982

21) 7812 25) No sum

26) -4

24 27)

5

3 28)

2

29) 6

30) 4

31) 7, 12, 17, 22, 27 32) 2, 3, -1, 4, -5

33) 3, 5, 8, 12

34) -10, -8, -5, -1

35) -9, -7, -4, 0

36) -13, -4, 5, 14

37) -2, -8, -32, -128, -512 38) 3, -15, 75, -375, 1875

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Algebra 2

ID: 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, ...

5 7 9 11 2) 3, , , , , ...

4 9 16 25

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

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) a = 6, d = 2 1 Find a 22

6) a = -39, d = -3 1 Find a 39

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) a = -1, r = -2 1 Find a 11

10) a = -4, r = 3 1 Find a 11

Find the missing term or terms in each geometric sequence.

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

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

Evaluate each arithmetic series described.

10

13) (7k - 12)

k = 3

10

14) (8m - 5)

m = 5

15) a = -10, d = -10, n = 13 1

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

16) a = 6, d = -2, n = 9 1

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

Determine the number of terms n in each arithmetic series.

19) a = 5, a = 65, S = 455

1

n

n

20) a = 15, a = 35, S = 150

1

n

n

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Evaluate each geometric series described. 21) -4 - 24 - 144 - 864..., n = 6

11 1 1 22) - + - + ..., n = 7

4 8 16 32

9

23) 4n - 1

n = 1

8

24)

5m - 1

m = 1

Evaluate each infinite geometric series described.

( ) 27 4 m - 1

25)

m = 1 32 3

( ) 27 2 n - 1

26) - n=1 2 3

33 3 27) 3 + + + ...

4 16 64

28) -1.3 - 1.04 - 0.832 - 0.6656...

Determine the number of terms n in each geometric series.

29) a = -4, r = -6, S = -124

1

n

30) a = -1, r = 2, S = -7

1

n

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

31) a = a - 7 n+1 n a = -40 1

32) a = a - 2 n+1 n a = 30 1

2 + a

33) a =

n

n + 1

2

a = -22 1

34) a = a + n n+1 n a = -6 1

35) a = a 2 n+1 n a =1 1

36) a = na

n + 1

n

a = -1 1

37) a = a -4 n+1 n a =1 1

38) a = a -5 n+1 n a = -3 1

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Answers to Sequences/Series Test Practice (ID: 2)

1) -128, 256, -512

13 15 17 2) , ,

36 49 64

3) 9375, 46875, 234375

4) 36, 49, 64 8) 101, 201, 301, 401 12) 15, 75, 375, 1875

5) a = 48 22

9) a = -1024 11

13) 268

6) a = -153 39

10) a = -236196 11

14) 330

7) 26, 20, 14 11) 12, 72, 432, 2592 15) -910

16) -18

17) 24

18) 182

19) 13

20) 6

21) -37324

43 22) -

256

23) 87381

24) 97656

25) No sum

81 26) -

2

27) 4

28) -6.5

29) 3

30) 3

31) -40, -47, -54, -61, -68 32) 30, 28, 26, 24, 22 33) -22, -10, -4, -1

34) -6, -4, -1, 3

35) 1, 2, 4, 8

36) -1, -2, -6, -24

37) 1, -4, 16, -64, 256

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

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Algebra 2

ID: 3

Name___________________________________

Sequences/Series Test Practice

Date________________ Period____

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

1) 4, 16, 36, 64, 100, ...

2) 6.2, 9.1, 12, 14.9, 17.8, ...

1 7 8 25 17 3) - , , , , , ...

363 6 3

33 3 3 4) 3, - , , - , , ...

5 25 125 625

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

5) a = 7, d = -3 1 Find a 20

6) a = -38, d = -4 1 Find a 20

Find the missing term or terms in each arithmetic sequence.

7) ..., 33, ___, ___, ___, ___, 83, ...

8) ..., -39, ___, ___, ___, ___, -79, ...

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

9) a = -2, r = -3 1 Find a 12

10) a = 2, r = -2 1 Find a 12

Find the missing term or terms in each geometric sequence.

11) ..., -3, ___, ___, ___, -243, ...

12) ..., 3, ___, ___, ___, ___, 3072, ...

Evaluate each arithmetic series described.

7

13) (16 - 9m)

m = 2

11

14) (1 - 8m)

m = 3

15) a = 30, d = 6, n = 15 1

16) a = 33, d = 9, n = 11 1

17) 18 + 28 + 38 + 48..., n = 20

18) 25 + 34 + 43 + 52..., n = 10

Determine the number of terms n in each arithmetic series.

19) a = 32, a = 344, S = 7520

1

n

n

20) a = 10, a = 58, S = 238

1

n

n

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Evaluate each geometric series described. 22 2

21) 2 - + - ..., n = 7 3 9 27

22) -2 - 10 - 50 - 250..., n = 7

7

23)

3m - 1

m = 1

10

24) 3k - 1

k = 1

Evaluate each infinite geometric series described.

25) -9.1 0.2m - 1

m = 1

26) 7.7 (-0.6)i - 1

i = 1

62 2 2 27) - + - + ...

5 5 15 45

28) 5.9 + 9.44 + 15.104 + 24.1664...

Determine the number of terms n in each geometric series.

29) a = 4, r = -4, S = 52

1

n

30) a = -1, r = -5, S = 104

1

n

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

31) a = a + 100 n+1 n a =6 1

32) a = a + 3 n+1 n a = -21 1

33) a = a + 7 n+1 n a = 11 1

34) a = a + 4 n+1 n a = 35 1

35) a = na

n + 1

n

a =1 1

3 36) a = a +

2 n + 1 n

12

a =-

1

7

37) a = a -4 n+1 n a =1 1

38) a = a -5 n+1 n a =2 1

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