Number Patterns

  Practical Learning Activity
Learn
Kyndeler Site Favicon 128 by 128
Practical

Read and learn about arithmetic sequences. Takes notes and answer questions.

(Free Counting 1-100 in Words and Numbers Worksheets)

Number Patterns

Arithmetic Sequences

Examples of Arithmetic Sequences

An arithmetic sequence is a sequence of numbers or terms that show a repeated mathematical pattern where the same amount is added or subtracted again and again.

Here are three examples of arithmetic sequences. In the first, 3 is added each time, to create each successive number in the sequence. In the second, 4 is added each time. In the third, a decreasing arithmetic sequence, 5 is subtracted each time.

Arithmetic Sequence Example 1: {1, 4, 7, 10, 13, …}

number line sequence adding 3

Arithmetic Sequence Example 2: {1, 5, 9, 13, 17, …}

number line sequence adding 4

Arithmetic Sequence Example 3: {12, 7, 2, -3, …}

number line sequence subtracting 5

The examples above show that within each arithmetic sequence, the same amount, known as the common difference, is always added or subtracted. This makes a number pattern. We can easily work out the next numbers in a sequence, by looking at how far apart the numbers are. For instance, in the second example, above, since the numbers in this sequence are 4 apart, we know that the number which is being added each time must be 4, and thus we know that the next number in the sequence after 17 will be 17 plus 4, which is 21.

Here is another example of an arithmetic sequence, {0, 2, 4, 6, 8, 10, …}. How far apart are the numbers? See if you can work out the next two numbers in the sequence.

Infinite sequences are written with three dots after the numbers as shown, {1, 2, 3, 4, 5, … }. These three dots indicate that the sequence is infinite and continues on and on forever. Three dots are used because it would take up too much space to write a very long list of numbers. Braces {} are used to surround a sequence.

See if you can work out the patterns in the following arithmetic sequences.

Exercise 1:

  • The arithmetic sequence illustrated below is $$\{0, 2, 4, 6, 8, …\}$$In this sequence, which number is being added each time to get each new number? If you continue the sequence beyond 8, what will the next two numbers in the sequence be?

    Show Answer
    $$2\;is\;being\;added\;each\;time.$$$$\;The\;next\;two\;numbers\;$$$$will\; be\;10\;and\; 12.$$
    • Qu1

    Exercise 2:

  • The arithmetic sequence shown below is $$\{0, 5, 10, 15, 20, …\}$$In this sequence, which number is being added each time to get each new number?

    Show Answer
    $$5\;is\;being\;added\;each\;time.$$
    • qu2

    Exercise 3:

  • The arithmetic sequence shown below is $$\{19, 16, 13, 10, 7, …\}$$In this sequence, which number is being subtracted each time? If you continue the sequence downwards beyond 7, what will the next two numbers in the sequence be?

    Show Answer
    $$3\; is \;being \;subtracted\;each \;time.$$$$ \;The\;next\;two\;numbers\;$$$$will\; be\;4\;and\; 1.$$
    • qu3

    Exercise 4:

  • The arithmetic sequence shown below is $$\{19, 15, 11, 7, 3, …\}$$In this sequence, which number is being subtracted each time? If you continue the sequence downwards beyond 3, what will the next number in the sequence be?

    Show Answer
    $$4\; is \;being \;subtracted\;each\;time. $$$$\;The\;next\;number\;$$$$will\; be\;-1.\;$$
    • qu4

    Exercise 5:

  • The arithmetic sequence shown below is $$\{0, 4, 8, 12, 16, …\}$$In this sequence, which number is being added each time? What will the next two numbers in this sequence be after 16, if you continue the sequence?

    Show Answer
    $$4\; is \;being \;added\;each\;time. $$$$\;The\;next\;two\;numbers\;$$$$will\; be\;20\;and\; 24.$$
    • qu5

    Exercise 6:

  • The arithmetic sequence illustrated below is $$\{0, 3, 6, 9, 12, …\}$$In this sequence, which number is being added each time to get each new number? If you continue the sequence upwards beyond 12, what will the next three numbers in the sequence be?

    Show Answer
    $$3\;is\;being\;added\;each\;time.$$$$\;The\;next\;three\;numbers\;$$$$will\; be\;$$$$15,\; 18\;and\; 21.$$
    • qu6

    Exercise 7:

  • The arithmetic sequence shown below is $$\{16, 14, 12, 10, 8, …\}$$In this sequence, which number is being subtracted each time to get each new number? If you continue the sequence downwards beyond 8, what will the next two numbers in the sequence be?

    Show Answer
    $$2\;is\;being\;subtracted\;each\;time.$$$$ \;The\;next\;two\;numbers\;$$$$will\; be\;6\;and\;4.$$
    • qu7

    Exercise 8:

  • The arithmetic sequence shown below is $$ \{-1, 3, 7, 11, 15, …\}$$In this sequence, which number is being added each time? If you continue the sequence upwards beyond 15, what will the next two numbers in the sequence be?

    Show Answer
    $$4\; is \;being \;added\;each \;time.$$$$ \;The\;next\;two\;numbers\;$$$$will\; be\;19\;and\;23.$$
    • qu8

    Exercise 9:

  • The arithmetic sequence shown below is $$\{19, 16, 13, 10, 7, …\}$$In this sequence, which number is being subtracted each time? What will the next number in this sequence be after 7, if you continue the sequence downwards?

    Show Answer
    $$3\; is \;being \;subtracted\;each\;time. $$$$\;The\;next\;number\;$$$$will\; be\;4.\;$$
    • qu9

    Exercise 10:

  • The arithmetic sequence shown below is $$\{-1, 1, 3, 5, 7, …\}$$In this sequence, which number is being added each time? If you continue the sequence upwards beyond 7, what will the next two numbers in the sequence be?

    Show Answer
    $$2\; is \;being \;added\;each\;time. $$$$\;The\;next\;two\;numbers\;$$$$will\; be\;9\;and\; 11.$$
    • qu10

    Free Counting 1-100 in Words and Numbers Worksheets 3 pages free downloadable printable PDF – Click on the link below to download

    Numbers 1- 100 in words and numbers worksheet

    (Go to the Maze Run Game)

    (Go to the Free Downloads page)

    (Go to the Tell the Time page)

    (Go to the Reading page)

    (Go to the Times Tables page)

    (Go to the Home page)