Arithmetic Sequences and Linear Functions

Sequences

A sequence is an ordered list of numbers. Each number in a sequence is called a term. Each term an has a specific position n in the sequence.

example: 5, 10, 15, 20, 25,…a_n

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.

Term

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)

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

Ready to try some examples?

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

Multiple Choice

What is the lesson about?

• Arithmetic Sequences

• Geometric Sequences

• No idea

• Some math stuff

Multiple Choice

What is each number in a sequence called?

• common difference

• term

• sequence

• arithmetic

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

Is the sequence arithmetic: 37, 31, 25, 19, ...

• Yes
• No

Multiple Select

Which sequences are arithmetic?

(hint: select 2)

• 2, 4, 6, 8, 10 ...

• 5, 10, 20, 40, 80, 100 ...

• 1, 3, 7, 9, 15, 20 ...

• 4, 8, 12, 16, 20, 24 ...

Fill in the Blanks

Fill in the blank: What is the next number in the arithmetic sequence?

2, 8, 14, 20,

Multiple Choice

If the first term of an arithmetic sequence is 5 and the common difference is 6, what are the first five terms?

• 5, 11, 17, 23, 29

• 6, 11, 16, 21, 26

• 5, 10, 15, 20, 25

• 5, 11, 15, 20, 26

Multiple Choice

Which sequence has a common difference of 4?

• 4, 6, 8, 10, 12...

• 1, 5, 9, 13, 17....

• 4, 4, 4, 4, 4...

• 4, 14, 24, 34, 44...

Multiple Choice

Is the sequence Arithmetic?

10, 18, 26, 34, 40

• Yes

• No

Fill in the Blanks

Fill in the blank: What is the next number in the arithmetic sequence.

2, 8, 14, 20,

Poll

Do you understand what an arithmetic sequence is?

• Yes

• A little bit

• No

• Mayber