Free Printable Recursive Formula

1.

Find the next three terms:
5, 8, 11, 14...

a)

16, 19, 22

b)

17, 19, 21

c)

17, 20, 23

d)

16, 18, 20

2.

Given the first five terms, write the recursive formula.
15, 12, 9, 6, 3 ....

a)

u₁ = 15
u_n = u_n-1 + 3

b)

u₀ = 15
u_n = u_n-1 + 3

c)

u₁ = 15
u_n = u_n-1 - 3

d)

u₀ = 15
u_n = u_n-1 - 3

3.

Write the recursive formula for 6, 17, 28, 39, 50....

a)

a_n=a_n-1+11
a₁=6

b)

a_n=a_n-1-4
a₁=6

c)

a_n=a_n-1+9
a₁=6

d)

a_n=a_n-1+6
a₁=6

4.

Given the recursive formula, find the first four terms:
a_n = a_n-1 + 5
a₁ = -16

a)

-16, -21, -26, -31

b)

5, -11, -27, -43

c)

-16, -80, -500, -200

d)

-16, -11, -6, -1

5.

The next two terms of the sequence 2,-4, 8,-16 are

a)

32, 64

b)

32, -64

c)

-64, 108

d)

32, 20

6.

Determine the first 3 terms of the following sequence.
t1= -3
tn=3tn-1

a)

-3, 9, 27

b)

-3, -9, -27

c)

-3, -6, -9

d)

-3, 6,9

7.

Determine the 3rd term of the sequence.

a₁=5

a_n= 2a_n-1- 1

a)

14

b)

13

c)

17

d)

16

8.

Write a recursive formula for the following sequence:

16,8, 4, 2,...

a)

a₁=16

a_n=2a_n-1

b)

a₁=16

a_n=.5a_n-1

c)

a₁=16

a_n=a_n-1 + .5

d)

a₁=16

a_n=a_n-1+ 2

9.

Given the recursive formula below, find the first five terms.

u₁ = 3

u_n = u_n-1 + 2

a)

3, 5, 7, 9, 11

b)

5, 7, 9, 11, 13

c)

2, 4, 6, 8, 10

d)

1, 3, 5, 7, 9

10.

Given the recursive formula below, write the first three terms.

a₁ = 4

a_n= 2a_n-1 + 5

a)

7, 19, 43

b)

4, 9, 14

c)

4, 13, 31

d)

1, 7, 19

11.

Determine if the following sequence is arithmetic or geometric.

4, 9, 14, 19, 24, ...

a)

Arithmetic

b)

Geometric

12.

Determine if the following sequence is arithmetic or geometric.

6, 12, 24, 48, 96, ...

a)

Arithmetic

b)

Geometric

13.

Identify the common difference of the given arithmetic sequence.

5, 1, -3, -7, ...

a)

d = -4

b)

d = -5

c)

d = 5

d)

d = 7

14.

Identify the common ratio for the given geometric sequence.

2, 6, 18, 54, 162, ...

a)

r = 4

b)

r = 3

c)

r = $\frac{1}{4}$

d)

r = 12

15.

Which of the following recursive formulas represents the given sequence.

4, 12, 20, 28, 36, ...

a)

$a_1=4$ , $a_n=a_{\left(n-1\right)}\cdot3$

b)

$a_1=4$ , $a_n=a_{\left(n-1\right)}+8$

c)

$a_1=4$ , $a_n=a_{\left(n-1\right)}-8$

d)

$a_1=4$ , $a_n=a_{\left(n-1\right)}\cdot9$

16.

Which of the following recursive formulas represents the given sequence.

7, 14, 28, 56, 112, ...

a)

$a_1=7$ , $a_n=a_{\left(n-1\right)}+7$

b)

$a_1=7$ , $a_n=a_{\left(n-1\right)}\cdot7$

c)

$a_1=7$ , $a_n=a_{\left(n-1\right)}\cdot2$

d)

$a_1=7$ , $a_n=a_{\left(n-1\right)}+14$

17.

Find the first four terms of the sequence given the rule:

a₁ = 10: a_n = 3a_n-1

a)

3, 9, 27, 81

b)

10, 30, 90, 270

c)

10, 13, 16, 19

d)

30, 90, 270, 810

18.

Find the 4th term for the sequence defined by a₁=9; a_n=a_n-1+8

a)

35

b)

17

c)

41

d)

33

19.

Find the 4th term for the sequence f(1)=3, f(n)=f(n-1)+5

a)

3

b)

8

c)

15

d)

18

20.

Each individual number in a sequence of numbers is called what?

a)

Common difference

b)

Successive term

c)

Term

d)

Geometric term

21.

What does a₁ represent?

a)

Any term

b)

First term

c)

Last term

22.

Identify the rule as recursive or explicit, then find the first 4 terms of the sequence.
a₁ = 100; a_n = a_n-1 - 8

a)

Explicit; 100, 92, 84, 76

b)

Recursive; 100, 92, 84, 76

c)

Explicit; 100, 108, 116, 124

d)

Recursive; 100, 108, 116, 124

23.

What is the recursive rule for the sequence:

2, 6, 18, 54...

a)

f(1)=3, f(n)=2f(n-1)

b)

f(1)=2, f(n)=4f(n-1)

c)

f(1)=3, f(n)=2f(n-1)

d)

f(1)=2, f(n)=3f(n-1)

24.

Find the next three terms: 4, 12, 36, 108, ...

a)

324, 972, 2916

b)

972, 2916, 8748

c)

405, 1215, 3645

25.

Find the 3rd term for the sequence f(1)=3, f(n)=-4*f(n-1)

a)

3

b)

-12

c)

-48

d)

48

Recursive Formula

Total questions: 25

Worksheet time: 1hrs 22mins

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