Introduction to Arithmetic Series

Arithmetic Sequences

Arithmetic sequences are all about finding patterns.

Poll

What number do you think comes next?

5, 10, 15, 20, ...

• 30

• 25

• 15

• 100

Poll

What number do you think comes next?

1, 3, 5, 7, ...

• 1

• 4

• 9

Arithmetic Sequence

A sequence of numbers with a common difference.

In other words... the pattern (or rule) is add or subtract the same number.

Here are two examples of arithmetic sequences.

• The first has a common difference of positive 6

• The second has a common difference of negative 5

Multiple Choice

Identify the common difference.

10, 20, 30, 40, ...

• 5

• 10

• 15

• 20

Multiple Choice

Find the common difference: 1, 201, 401, 601, ...

• d = 100

• d = 101

• d = 200

• d = 201

If the common difference isn't obvious...

You can subtract two consecutive terms (terms right next to each other) to help find it!

Multiple Choice

Identify the common difference.

3, 7, 11, 15, ...

HINT: You can find the common difference by subtracting: 7 - 3 or 11 - 7

• 6

• 5

• 4

• 2

Multiple Choice

Identify the common difference.

97, 86, 75, 64, ...

• 8

• 11

• -11

• -8

Multiple Choice

Find the common difference: 29, 21, 13, 5, ...

• d = -10

• d = -9

• d = -8

• d = -7

Multiple Choice

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

• -3

• -1

• -2

• 3

Multiple Choice

The next two terms of the sequence 12 ,17, 22, ... are

HINT: Find the common difference (maybe by subtracting) and use that to keep the pattern going!

• 28 and 33

• 29 and 34

• 27 and 32

• 30 and 35

Multiple Choice

The next two terms of the sequence 4, 7, 10, 13, ... are

• 16 and 19

• 15 and 19

• 16 and 18

• 15 and 18

Multiple Choice

Find the next three terms in the arithmetic sequence: 25, 34, 43, 52, ...

• 63, 72, 81

• 79, 88, 97

• 70, 79, 88

• 61, 70, 79

Multiple Choice

What is the common difference of the following sequence?

7, 27, 47, 67,...

• 10

• 20

• 3

• -20

Multiple Choice

Which sequence is NOT an arithmetic sequence?

Hint: Find one that does not have an add or subtract pattern.

• 12, 18, 24, 30,...

• 10, 3, -4, -11,...

• 2, 4, 8, 16,...

• 16, 20, 24, 28,...

Multiple Choice

Which sequence is NOT an arithmetic sequence?

Hint: Find one that does not have an add or subtract pattern.

• -7, -13, -19, -25,...

• -10, -6, -2, 2,..

• 6, 8, 10, 12,...

• 3, 15, 75, 375,...

Multiple Choice

The first three terms of an arithmetic sequence are as follows.

3, -4, -11, ...

Find the next two terms of this sequence

• -17 and -25

• -18 and -26

• -18 and -25

• -17 and -26

Multiple Choice

The next term of the sequence 11, 8, 5, 2, ... is:

• -1

• -2

• 1

• 2