Free Printable Arithmetic Sequences Review

1.

Find a₂₆ in the arithmetic sequence: -15, -35, -55, -75, ...

a)

-515

b)

-490

c)

-535

d)

460

2.

Find the first term of the given sequence:
a₁₄=68
d=3

a)

14

b)

20

c)

26

d)

29

3.

Given the sequence:
25, 21, 17, 13,...
Write the explicit equation that models the sequence. (Hint: Simplify your equation.)

a)

a_n = 4n + 29

b)

a_n = -4n + 25

c)

a_n= -4n + 29

d)

a_n = 4n + 25

4.

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

5.

Find $a_{32}$ for the sequence.
9, 4, -1, -6, -11, ...

a)

81

b)

-34

c)

-146

d)

-225

6.

Write the explicit formula for the sequence containing $a_{26}=38$ and $a_{40}=94$

a)

$a_n=-66+4\left(n-1\right)$

b)

$a_n=-62+4\left(n-1\right)$

c)

$a_n=-58+4\left(n-1\right)$

d)

$a_n=-62+4n$

7.

Write the recursive formula for the sequence: $a_n=5-\frac{1}{2}n$

a)

$a_1=4.5\ \ \ \ \ \ \ a_n=a_{n-1}-\frac{1}{2}\ ,\ n\ge2$

b)

$a_1=5\ \ \ \ \ \ \ \ a_n=a_{n-1}-\frac{1}{2},n\ge2$

c)

$a_1=-\frac{1}{2}\ \ \ \ \ \ \ \ \ a_n=a_{n-1}+5,n\ge2$

d)

$a_1=5\ \ \ \ \ \ \ a_n=a_{n-1}+\frac{1}{2\ },\ n\ge2$

8.

Write the explicit formula for the sequence where $a_{42}=-18$ and $a_{96}=-288$

a)

$a_n=187-5n$

b)

$a_n=192-5n$

c)

$a_n=-270+5n$

d)

$a_n=-265+5n$

9.

Write the recursive formula for the arithmetic sequence with a difference of -4.5 and $a_{13}=-80$

a)

$a_1=26\ \ \ \ a_n=a_{n-1}-4.5,\ n\ge2$

b)

$a_1=-\ 138.5\ \ \ a_n=a_{n-1}-4.5,n\ge2$

c)

$a_1=-134\ \ \ \ \ a_n=a_{n-1}-4.5,\ n\ge2$

d)

$a_1=-26\ \ \ \ a_n=a_{n-1}-4.5,\ n\ge2$

10.

Find the common difference: -34, -29, -24, -19, ...

a)

d = -5

b)

d = 5

c)

d = -6

d)

d = 6

11.

What is the common difference of the sequence 2, -1, -4, -7,...?

a)

-3

b)

-1

c)

-2

d)

3

12.

Find the next three terms in the arithmetic sequence: -33, -24, -15, -6, ...

a)

-1, 7, 15

b)

-5, 2, 9

c)

3, 12, 21

d)

-65, -73, -81

13.

Write an explicit formula for the sequence 45, 40, 35, 30, ...

Hint: The sequence is arithmetic so use this formula: $a_n=a_1+d\left(n-1\right)$ .

a)

$a_n=45+5\left(n-1\right)$

b)

$a_n=45-5\left(n-1\right)$

c)

$a_n=5+45\left(n-1\right)$

d)

$a_n=5-45\left(n-1\right)$

14.

Find the 32nd term of this sequence.
34, 37, 40, 43, ...

a)

32

b)

64

c)

127

d)

356

15.

Write a recursive function for the following sequence. Note: The first number is the 1st term.

4, 1 , -2, -5, -8,...

a)

a₀= 4

a_n = a_n-1 - 3

b)

a₀= 7

a_n = a_n-1 -3

c)

a₀= 7

a_n = a_n-1 + 3

d)

y = 3x - 4

Arithmetic Sequences Review

Total questions: 15

Worksheet time: 1hrs 9mins

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