Introduction to Sequences

Kuta Software - Infinite Algebra 2

Introduction to Sequences

Find the next three terms in each sequence. 1) 1, -3, 9, -27, 81, ...

Name___________________________________ Date________________ Period____

2) 9, 109, 209, 309, 409, ...

3) 0, 3, 8, 15, 24, ...

1131 5 4) , , , , , ...

2 2 8 4 32

5) 4, 16, 36, 64, 100, ...

6) 14, 34, 54, 74, 94, ...

555 5 7) 5, , , , , ...

2 4 8 16

Find the tenth term in each sequence. 2 7 17

9) -1, , , 4, , ... 33 3

11) -2, -6, -18, -54, -162, ... 13) -4, 12, -36, 108, -324, ...

15) -28, 172, 372, 572, 772, ...

Find the first four terms in each sequence.

2n + 1

17) a = n

3

n

19)

a

=

2

n

+

1

n

8) -9, 101, -999, 10001, -99999, ...

10) 7, 9, 12, 16, 21, ... 12) -23, -18, -13, -8, -3, ...

3 14) -6, -2, 0, 1, , ...

2 16) 37, 46, 55, 64, 73, ... 18) a = 3n - 1

n 3

n 20) a =

n 2n + 1

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Worksheet by Kuta Software LLC

Find the tenth term in each sequence.

2n + 1

21) a = n

3

n

23) a = (2n)2 n

22) a = 4n - 1 n

24) a = (2n - 1)2 n

Find the first four terms in each sequence. 25) a = a + 10

n n-1

a = 29 1

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

Find the tenth term in each sequence.

29) a = na

n

n - 1

a = -1 1

31) a = a 3 n n-1 a = -3 1

26) a = a 2

n

n - 1

a = -1 1

2 + a

28) a =

n - 1

n

2

a = 10 1

30) a = a + 10

n

n - 1

a = 11 1

2 + a

32) a =

n - 1

n

2

a = -14 1

Write the explicit formula for each sequence. 33) -12, -9, -6, -3, 0, ...

36 34) -6, -3, -2, - , - , ...

25

Write the recursive formula for each sequence. 35) 2, 4, 7, 11, 16, ...

36) 15, 215, 415, 615, 815, ...

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Worksheet by Kuta Software LLC

Kuta Software - Infinite Algebra 2

Introduction to Sequences

Find the next three terms in each sequence. 1) 1, -3, 9, -27, 81, ...

-243, 729, -2187

3) 0, 3, 8, 15, 24, ... 35, 48, 63

5) 4, 16, 36, 64, 100, ... 144, 196, 256

555 5 7) 5, , , , , ...

2 4 8 16 55 5

, , 32 64 128 Find the tenth term in each sequence.

2 7 17 9) -1, , , 4, , ...

33 3 a = 14

10

11) -2, -6, -18, -54, -162, ... a = -39366

10

13) -4, 12, -36, 108, -324, ... a = 78732

10

15) -28, 172, 372, 572, 772, ... a = 1772

10

Find the first four terms in each sequence.

2n + 1 5 7 9

17) a = n

3

n

3, , , 8 27 64

19)

a

=

2

n

+

1

n

2, 5, 10, 17

Name___________________________________ Date________________ Period____

2) 9, 109, 209, 309, 409, ... 509, 609, 709

1131 5 4) , , , , , ...

2 2 8 4 32

371

n

, , ; Note: a =

32 128 32

n 2n

6) 14, 34, 54, 74, 94, ... 114, 134, 154

8) -9, 101, -999, 10001, -99999, ... 1000001, -9999999, 100000001

10) 7, 9, 12, 16, 21, ... a = 61

10

12) -23, -18, -13, -8, -3, ... a = 22

10

3 14) -6, -2, 0, 1, , ...

2 127 a= 10 64 16) 37, 46, 55, 64, 73, ... a = 118

10

18) a = 3n - 1 n 1, 3, 9, 27

3

n

1 8 27 64

20) a =

,, ,

n 2n + 1 3 5 7 9

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Worksheet by Kuta Software LLC

Find the tenth term in each sequence.

2n + 1

21) a = n

3

n

21 a= 10 1000

23) a = (2n)2 n a = 400 10

22) a = 4n - 1 n a = 262144 10

24) a = (2n - 1)2 n a = 361 10

Find the first four terms in each sequence.

25) a = a + 10 n n-1 a = 29 1 29, 39, 49, 59

27) a = a + n n n-1 a = -4 1 -4, -2, 1, 5

Find the tenth term in each sequence.

29) a = na

n

n - 1

a = -1 1

a = -3628800 10

31) a = a 3 n n-1 a = -3 1

a = -59049 10

Write the explicit formula for each sequence.

33) -12, -9, -6, -3, 0, ...

a = -15 + 3n

n

26) a = a 2

n

n - 1

a = -1 1

-1, -2, -4, -8

2 + a

28) a =

n - 1

n

2

a = 10 1

10, 6, 4, 3

30) a = a + 10

n

n - 1

a = 11 1

a = 101 10

2 + a

32) a =

n - 1

n

2

a = -14 1

63 a=

10 32

36

6

34) -6, -3, -2, - , - , ... a = -

25

n n

Write the recursive formula for each sequence.

35) 2, 4, 7, 11, 16, ...

36) 15, 215, 415, 615, 815, ...

a =a +n

n

n - 1

a =2 1

a = a + 200

n

n - 1

a = 15 1

Create your own worksheets like this one with Infinite Algebra 2. Free trial available at

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