Intro to Arithmetic Sequence

​Arithmetic Sequences

By Penny Turner

• What is an arithmetic sequence?

• How do you find the common difference?

• How do you find the "nth" term in a sequence?

Sequences

A sequence is an ordered list of numbers. Each number in a sequence is called a term.

Consider the list of numbers: 2, 5, 8, 11, 14...

The first term is.....______
(NEXT ...)

Drag and Drop

Consider the list of numbers: 2, 5, 8, 11, 14...
The first term is...

Placeholder

The second term is..​

Placeholder

Drag these tiles and drop them in the correct blank above

2

5

3

8

In a sequence each number is called a term.

The dots at the end mean the sequence continues forever.

a₁ is the first term

a₂ is the second term

a₃ is the third term and so on...

a_n is the nth term (we will find the equation for the nth term in the next lesson)

​Sequences

Dropdown

Consider the list of numbers: 2, 5, 8, 11, 14...
The first term is labeled a₁ =2

The second term is labeled​ a₂ = 5

Identify what number is labeled a₅ =​

Select answer

Arithmetic Sequence

An arithmetic sequence is a sequence where you add a constant number to find the next term, similar to the constant rate of change in a linear function.

In an arithmetic sequence we only add to find the next number (term). This number can be positive or negative.

Common Difference

The number you add/subtract to find the next term in a sequence is called the common difference.

Subtract two terms to find the common difference. d is used to define the common difference

HOW to find the common difference?

Remember in an arithmetic sequence, each number is found by adding a common difference, which can be positive or negative.

Take the 2nd number and subtract a 1st number.

2nd number 7 - 1st number 3 = common difference 4

Common Difference =
2nd number - 1st number

45 - 50 = -5
The common difference of this arithmetic sequence is -5.
-5 was added
(which is same as subtracting 5)

EXAMPLE:

​Non-Examples of Arithmetic Sequence

Add 8
Add 8
Add -7
Add 1
Add -4.5

Add 3, then 4, then 5, then 6
Pattern: Postive then Negative
Add 2, 2, 2, 2, 3
Add -20, -10, -5
Add 3, 5, 7

Ready to do some practice?

Multiple Choice

What is the difference between two numbers in an arithmetic sequence called?

• common difference

• term

• sequence

• number

Multiple Choice

Identify the common difference.

10, 20, 30, 40, ...

• 5

• 10

• 15

• 20

Multiple Choice

The next two terms of the sequence 12,17,22,27 are

• 28 and 33

• 29 and 34

• 32 and 37

• 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 common difference: 29, 21, 13, 5, ...

Remember, the common difference is the difference between the numbers.

• d = -10

• d = -9

• d = -8

• d = -7

Multiple Choice

What is the next number in the sequence 3,5,7,9...

• 11

• 10

• 13

• 12

Multiple Choice

What is the next number in the sequence 20,40,60,80...

• 100

• 90

• 80

• 95

Multiple Choice

What is the next number in the sequence 15,22,29,36...

• 43

• 45

• 42

• 41

Multiple Choice

Is the sequence arithmetic: -3, 3, -3, 3, ...

• Yes

• No

Multiple Choice

The common difference for this sequence 18, 15, 12, 9, 6, 3, 0 is...

• 3

• - 5

• - 3

• 7

Math Response

Type in the common difference:

21, 19, 17, 15, …

Type answer here

Correct Answer: -2

Deg^°

Rad

Multiple Choice

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

• -1, 7, 15
• -5, 2, 9
• 3, 12, 21
• -65, -73, -81

Multiple Choice

Identify the common difference.
3, 7, 11, 15, ...

• 6
• 5
• 4
• 2

Multiple Choice

Describe the pattern in the sequence. Find the next three terms.

13, 15, 17, 19,...

• Add 2; 23, 25, 27

• Multiply by 2; 38, 76, 152

• Add -2; 17, 15, 13

• Add 2; 21, 23, 25

Multiple Choice

Find the next four terms of the arithmetic sequence 16, 24, 32,...

• 40, 48, 56, 64

• 36, 40, 44, 48

• 35, 40, 45, 50

• 40, 44, 50, 56