# Understand Common Integer Sequences

In this worksheet, students will revise common integer sequences.

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Generate Terms of a Sequence

Difficulty level:

### QUESTION 1 of 10

The following important sequences should be familiar to you:

Counting numbers

1, 2, 3, 4, 5, 6, 7, 8...

Multiples of 2

2, 4, 6, 8, 10, 12, 14, 16...

Powers of 2

2, 4, 8, 16, 32, 64, 128, 256...

Powers of 10

10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000...

Fibonacci

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...

Square numbers

1, 4, 9, 16, 25, 36, 49, 64...

Cube numbers

1, 8, 27, 64, 125, 216, 343, 512...

Triangle numbers

1, 3, 6, 10, 15, 21, 28, 36, 45...

Now let's consolidate your knowledge of these sequences by tacking some questions!

Write down the next three terms in the following sequence:

What are the next three terms in the following sequence?

2, 4, 6, 8, 10...

12

16

14

18

What are the next three terms in the following sequence?

2, 4, 8, 16, 32...

64, 96, 128

40, 48, 56

64, 128, 256

34, 36, 38

Write down the next three terms in the following sequence:

1, 4, 9, 16, 25...

64, 96, 128

40, 48, 56

64, 128, 256

34, 36, 38

Look at the sequence below.

1, 1, 2, 3, 5

What are the next three numbers in the sequence?

8, 13, 21

7, 9, 11

8, 11, 14

Write down the next three terms in the sequence below.

10, 100, 1000, 10000...

8, 13, 21

7, 9, 11

8, 11, 14

What are the three terms in the following sequence?

1, 3, 5, 7, 9...

10, 12, 14

11, 13, 15

10, 11, 12

81, 90, 99

What is the following number sequence?

0, 4, 8, 12, 16

Multiples of 4

Even numbers (ascending)

Even numbers (descending)

Multiples of 2

Can you identify the mistake in the next three terms of the following sequence?

3, 9, 27, 81...

243, 720, 2187

What are the next three terms in the following sequence?

1, 3, 6, 10, 15...

21, 28, 36

20, 25, 30

• Question 1

Write down the next three terms in the following sequence:

EDDIE SAYS
This first question was just a warm-up for you! The sequence ascends (goes up) by +1 each step. Therefore the missing values are 1, 2 and 3.
• Question 2

What are the next three terms in the following sequence?

2, 4, 6, 8, 10...

12
16
14
EDDIE SAYS
In this question, the sequence is going up in multiples of 2, making the following values in the sequence 12, 14 and 16. Although 18 is part of that number sequence the question asks only for the next three terms. You must read each question carefully to ensure you don't get caught out.
• Question 3

What are the next three terms in the following sequence?

2, 4, 8, 16, 32...

64, 128, 256
EDDIE SAYS
This sequence increases in powers of 2, meaning each number is its previous value doubled. Therefore, option 3 is the correct answer as: 32 x 2 = 64 64 x 2 = 128 128 x 2 = 256 Is this starting to make sense?
• Question 4

Write down the next three terms in the following sequence:

1, 4, 9, 16, 25...

EDDIE SAYS
This number sequence is each squared number. That is: 1 x 1 = 1 2 x 2 = 4 3 x 3 = 9 4 x 4 = 16 5 x 5 = 25 6 x 6 = 36 7 x 7 = 49 8 x 8 = 64 Did you find that easier or more difficult than the previous question?
• Question 5

Look at the sequence below.

1, 1, 2, 3, 5

What are the next three numbers in the sequence?

8, 13, 21
EDDIE SAYS
The sequence is actually Fibonacci's numbers, therefore option 1 is the correct answer. Fibonacci's numbers is a sequence beginning with 1, where each number is made up of the two numbers before it added together. 1 1 1 + 1 = 2 1 + 2 = 3 2 + 3 = 5 3 + 5 = 8 5 + 8 = 13 8 + 13 = 21 and so on...
• Question 6

Write down the next three terms in the sequence below.

10, 100, 1000, 10000...

EDDIE SAYS
This sequence went up in powers of 10. That is, you had to times each number by 10 in order to get the next value in the sequence. 10 x 10 = 100 100 x 10 = 1000 1,000 x 10 = 10,000 10,000 x 10 = 100,000 100,000 x 10 = 1,000,000 1,000,000 x 10 = 100,00,000 Great work if you spotted the pattern.
• Question 7

What are the three terms in the following sequence?

1, 3, 5, 7, 9...

11, 13, 15
EDDIE SAYS
This sequence was ascending (going up) odd numbers. Can you identify the patterns evident in options 1, 2 and 4?
• Question 8

What is the following number sequence?

0, 4, 8, 12, 16

Multiples of 4
EDDIE SAYS
The correct answer was multiples of 4. In this number sequence, you are going up in +4 each step. This means the next numbers in the sequence would be 20, 24 and 28. How did you get on?
• Question 9

Can you identify the mistake in the next three terms of the following sequence?

3, 9, 27, 81...

243, 720, 2187
EDDIE SAYS
In this sequence, we are going up in powers of 3. This means each step in the sequence should be 3 times the previous number. The value '720' is an error, it should read 729. 3 3 x 3 = 9 3 x 9 = 27 3 x 27 = 81 3 x 81 = 243 3 x 243 = 729 3 x 729 = 2,187 Great work if you spotted that!
• Question 10

What are the next three terms in the following sequence?

1, 3, 6, 10, 15...

21, 28, 36
EDDIE SAYS
This sequence is an example of triangle numbers! Strong finish, you've now ticked off another activity. Give yourself a pat on the back maths-whiz, that was seriously impressive.
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