Free Printable Recursive Sequences

1.

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

2.

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

3.

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)

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

4.

Determine the 3rd term of the sequence.

a₁=5

a_n= 2a_n-1- 1

a)

14

b)

13

c)

17

d)

16

5.

Write a recursive formula for the following sequence:

16,8, 4, 2,...

a)

a₁=16

a_n=a_n-1 (2)

b)

a₁=16

a_n=a_n-1 (1/2)

c)

a₁=16

a_n=a_n-1 + (1/2)

d)

a₁=16

a_n=a_{n-1 +} (2)

6.

Find the first four terms of the sequence.

a_n= 2a_(n-1)+ n where a₀= 0

a)

0, 0, 0, 0

b)

0, 1, 4, 11

c)

0, 1, 2, 4

d)

0, 2, 4, 8

7.

Which of the following sequences has the recursive rule g_n = g_n-1 * 1/5

a)

{17,22,27,32,37, …}

b)

{11,6,1,-4,-9, …}

c)

{7,35,175,875,4375, …}

d)

{21875,4375,875,175,35, …}

8.

Which of the following sequences has the recursive rule f_n = f_n-1 + f_n-2

a)

{8,12,16,20,24, …}

b)

{-15,-19,-23,-27,-31, …}

c)

{-3,-12,-48,-192,-768, …}

d)

{1, 2, 3, 5, 8, …}

9.

Given the recursive formula, find the explicit form
a_n = a_n-1 - 5
a₁ = 22

a)

a_n = 22 + (n-1)(-5)

b)

a_n = 22 + (n-1)(5)

c)

a_n = -5 + (n-1)(22)

d)

a_n = -16 + (n-1)(-5)

10.

Write a recursive rule for the sequence a_n = 17 + (n-1)(-16)

a)

a₁ = 17
a_n = a_n-1 + 16

b)

a₁ = 17
a_n = a_n-1 - 17

c)

a₁ = 17
a_n = a_n-1 - 15

d)

a₁ = 17
a_n = a_n-1 - 16

11.

Does this recursive routine model growth or decay, and by what percent?
U₁ = 10
U_n+1 = U_n*.75

a)

Growth, 75%

b)

Growth, 25%

c)

Decay, 75%

d)

Decay, 25%

12.

Write a recursive rule for the sequence 1, 2, 5, 14, 41, 122, …

a)

a_n = (a_n-1)² + 1

b)

a_n = 2 a_n-1 - 2

c)

a_n = 3 a_n-1 - 1

d)

a_n = 3 a_n-1 + 1

13.

What is the explicit form of the sequence $\frac{1}{2},\ \frac{2}{5},\ \frac{1}{3},\ \frac{2}{7},\ \frac{1}{4}\ ...$

a)

$a_n=\frac{2}{n+3}$

b)

$a_n=\frac{2}{n-3}$

c)

$a_n=\frac{n}{n-3}$

d)

$a_n=\frac{n}{n+3}$

e)

$a_n=\frac{2}{n}$

Recursive Sequences

Total questions: 13

Worksheet time: 39mins

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