Free Printable Sequences

1.

The next term of the sequence 2,4,8,16 are

a)

64

b)

32

c)

108

d)

20

2.

Use the explicit formula to find the first four terms of the sequence.
$a_n=9\cdot4^{\left(n-1\right)}$

a)

4, 36, 324, 2916

b)

9, 36, 144, 576

c)

9, 13, 17, 21

d)

4, -5, -14, -23

3.

Use the explicit formula to find the 7th term of the sequence.
$a_n=22-3\left(n-1\right)$

a)

4

b)

1

c)

18

d)

114

4.

Use the explicit formula to find the 3rd term of the sequence.
$a_n=128\cdot\left(\frac{1}{2}\right)^{\left(n-1\right)}$

a)

64

b)

32

c)

16

d)

8

5.

A sequence is _______.

a)

a set of numbers in a specific order.

b)

a formula used to find a number.

c)

the term after a_n.

d)

a collection of data.

6.

Write the recursive formula for 4, 8, 12....

a)

a_n=a_n-1-7

b)

a_n=a_n-1-4

c)

a_n=a_n-1+3

d)

a_n=a_n-1+4

7.

Write the recursive formula of 13, 9, 5...

a)

a_n=a_n-1-4

b)

a_n=a_n-1+3

c)

a_n=a_n-1-5

d)

a_n=a_n-1+4

8.

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

a)

a_n=a_n-1+11

b)

a_n=a_n-1-4

c)

a_n=a_n-1+9

d)

a_n=a_n-1+6

9.

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)

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

10.

Which of the following equations is explicit?

a)

f(n) = 4n + 5

b)

f(n) = f(n-1) x 5

11.

Which of the following equations is recursive?

a)

f(n) = f(n-1) +4

b)

f(n) = 2n - 5

12.

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

a)

{-12,-7,-2,3,8, …}

b)

{2,-3,-8,-13,-18, …}

c)

{-3,-15,-75,-375,-1875, …}

d)

{-9375,-1875,-375,-75,-15, …}

13.

Which of the following sequences has the recursive rule a_n = a_n-1 - 5

a)

{-19,-14,-9,-4,1, …}

b)

{9,4,-1,-6,-11, …}

c)

{-4,-20,-100,-500,-2500, …}

d)

{-12500,-2500,-500,-100,-20, …}

14.

Find the three terms in the sequence after the last one given.

-3, 9, -27, 81, ___, ___, ___,...

a)

$-243,\ 729,\ -2187$

b)

$243,\ 729,\ 2187$

c)

$108,\ 117,\ 126$

d)

$90,\ 99,\ 108$

15.

Find the 11th term using the explicit formula: f(n) = 3(n-4) + 6

a)

f(11) = 27

b)

f(11) = 23

c)

f(11) = 39

d)

f(11) = 25

16.

Write a recursive formula for the following sequence:

10, 5, 0, -5,...

a)

a₁= 10

a_n= a_n-1 - 5

b)

a₁= 10

a_n= a_n-1 + 5

c)

a₁= 10

a_n= a_n (5)

d)

a₁= 10

a_n= a_n-1 (5)

17.

Write the explicit formula for the sequence.

15, 22, 29, 36, 43, ...

a)

$a_n=15+\left(n-1\right)\left(22\right)$

b)

$a_n=15\cdot7^{\left(n-1\right)}$

c)

$a_n=15+\left(n-1\right)\left(7\right)$

d)

$a_n=29-14^{\left(n-1\right)}$

18.

Write the explicit formula for the sequence.

7, 28, 112, 448, ...

a)

$a_n=7+4\left(n-1\right)$

b)

$a_n=7\cdot4^{\left(n-1\right)}$

c)

$a_n=\frac{448}{4n}$

d)

$a_n=28+84\left(n-1\right)$

19.

Create the explicit formula for the sequence:
2, 8, 14, ...
(Hint: Write your formula and then simplify it.)

a)

a_n=2+6n

b)

a_n=-6+6n

c)

a_n=6n-4

d)

a_n=4-6n

20.

In a certain arithmetic sequence, a₅= 12 and a₆= 16. What is a₁?

a)

-8

b)

-4

c)

4

d)

8

Sequences

Total questions: 20

Worksheet time: 24mins

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