In the previous Eleven Plus maths quiz we asked you to create number sequences by following certain rules about the n^{th} term. How did you get on? In this quiz, the second of our medium level ones on the topic, we give you more chance to practice.

To create a number sequence from a given rule, all you have to do is apply the rule to each number. For example, if the rule is n^{th} term = 2n, the process to follow would be this:

- n = 1 gives 2 × 1 = 2
- n = 2 gives 2 × 2 = 4
- n = 3 gives 2 × 3 = 6
- n = 4 gives 2 × 4 = 8

Simple isn’t it? I’m glad you think so!

Have a go at this quiz and see whether or not you’ve mastered number sequences.

1.

Which sequence can be formed from the given rule for the n^{th} term?.

n^{th} term = 3n + 2

n

5, 8, 11, 14 ...

7, 9, 11, 14 ...

5, 9, 11, 14

5, 8, 11, 15

2.

Which sequence can be formed from the given rule for the n^{th} term?.

n^{th} term = -n + 3

n

4, 5, 6, 7 ...

2, 0, -2, -4 ...

2, 1, 0, -1 ...

1, 0, -1, -2 ...

The terms of the sequence are found by first putting n = 1, then n = 2, then n = 3 and finally n = 4 in the rule for the n^{th} term = -n + 3. As follows:

n = 1 gives -1 + 3 = 2

n = 2 gives -2 + 3 = 1

n = 3 gives -3 + 3 = 0

n = 4 gives -4 + 3 = -1

n = 1 gives -1 + 3 = 2

n = 2 gives -2 + 3 = 1

n = 3 gives -3 + 3 = 0

n = 4 gives -4 + 3 = -1

3.

Which sequence can be formed from the given rule for the n^{th} term?.

n^{th} term = 9n – 5

n

4, 13, 22, 31 ...

5, 14, 23, 32 ...

3, 12, 21, 30 ...

6, 15, 24, 33 ...

The terms of the sequence are found by first putting n = 1, then n = 2, then n = 3 and finally n = 4 in the rule for the n^{th} term = 9n -5. As follows (do the multiplication first THEN the subtraction):

n = 1 gives 9 × 1 - 5 = 4

n = 2 gives 9 × 2 - 5 = 13

n = 3 gives 9 × 3 - 5 = 22

n = 4 gives 9 × 4 - 5 = 31

n = 1 gives 9 × 1 - 5 = 4

n = 2 gives 9 × 2 - 5 = 13

n = 3 gives 9 × 3 - 5 = 22

n = 4 gives 9 × 4 - 5 = 31

4.

Which sequence can be formed from the given rule for the n^{th} term?.

n^{th} term = -4n

n

0, 4, 8, 12 ...

0, -4, -8, -12 ...

-4, -6, -8, -10

-4, -8, -12, -16 ...

The terms of the sequence are found by first putting n = 1, then n = 2, then n = 3 and finally n = 4 in the rule for the n^{th} term = -4n. As follows:

n = 1 gives -4 × 1 = -4

n = 2 gives -4 × 2 = -8

n = 3 gives -4 × 3 = -12

n = 4 gives -4 × 4 = -16

n = 1 gives -4 × 1 = -4

n = 2 gives -4 × 2 = -8

n = 3 gives -4 × 3 = -12

n = 4 gives -4 × 4 = -16

5.

Which sequence can be formed from the given rule for the n^{th} term?.

n^{th} term = 3n + 7

n

7, 10, 13, 16 ...

10, 15, 20, 25 ...

7, 14, 21, 28 ...

10, 13, 16, 19 ...

The terms of the sequence are found by first putting n = 1, then n = 2, then n = 3 and finally n = 4 in the rule for the n^{th} term = 3n + 7. As follows (do the multiplication first THEN the addition):

n = 1 gives 3 × 1 + 7 = 10

n = 2 gives 3 × 2 + 7 = 13

n = 3 gives 3 × 3 + 7 = 16

n = 4 gives 3 × 4 + 7 = 19

n = 1 gives 3 × 1 + 7 = 10

n = 2 gives 3 × 2 + 7 = 13

n = 3 gives 3 × 3 + 7 = 16

n = 4 gives 3 × 4 + 7 = 19

6.

Which sequence can be formed from the given rule for the n^{th} term?.

n^{th} term = 3n + 10

n

13, 16, 19, 22 ...

3, 6, 9, 12 ...

13, 15, 18, 21 ...

13, 16, 18, 22 ...

The terms of the sequence are found by first putting n = 1, then n = 2, then n = 3 and finally n = 4 in the rule for the n^{th} term = 3n + 10. As follows (do the multiplication first THEN the addition):

n = 1 gives 3 × 1 + 10 = 13

n = 2 gives 3 × 2 + 10 = 16

n = 3 gives 3 × 3 + 10 = 19

n = 4 gives 3 × 4 + 10 = 22

n = 1 gives 3 × 1 + 10 = 13

n = 2 gives 3 × 2 + 10 = 16

n = 3 gives 3 × 3 + 10 = 19

n = 4 gives 3 × 4 + 10 = 22

7.

Which sequence can be formed from the given rule for the n^{th} term?.

n^{th} term = 12n

n

1, 12, 24, 36 ...

12, 24, 36, 48 ...

12, 24, 38, 48 ...

12, 24, 36, 49 ...

The terms of the sequence are found by first putting n = 1, then n = 2, then n = 3 and finally n = 4 in the rule for the n^{th} term = 12n. As follows:

n = 1 gives 12 × 1 = 12

n = 2 gives 12 × 2 = 24

n = 3 gives 12 × 3 = 36

n = 4 gives 12 × 4 = 48

n = 1 gives 12 × 1 = 12

n = 2 gives 12 × 2 = 24

n = 3 gives 12 × 3 = 36

n = 4 gives 12 × 4 = 48

8.

Which sequence can be formed from the given rule for the n^{th} term?.

n^{th} term = n^{3}

n

1, 4, 9, 12 ...

1, 8, 27, 64 ...

3, 6, 9, 12 ...

3, 9, 16, 25 ...

The terms of the sequence are found by first putting n = 1, then n = 2, then n = 3 and finally n = 4 in the rule for the n^{th} term = n^{3}. As follows:

n = 1 gives 1^{3} = 1

n = 2 gives 2^{3} = 8

n = 3 gives 3^{3} = 27

n = 4 gives 4^{3} = 64

n = 1 gives 1

n = 2 gives 2

n = 3 gives 3

n = 4 gives 4

9.

Which sequence can be formed from the given rule for the n^{th} term?.

n^{th} term = 1.5n

n

0.5, 2, 3.5, 5 ...

1.5, 3, 4.5, 6 ...

3, 6, 9, 12 ...

15, 30, 45, 60 ...

The terms of the sequence are found by first putting n = 1, then n = 2, then n = 3 and finally n = 4 in the rule for the n^{th} term = 1.5n. As follows:

n = 1 gives 1.5 × 1 = 1.5

n = 2 gives 1.5 x 2 = 3

n = 3 gives 1.5 × 3 = 4.5

n = 4 gives 1.5 × 4 = 6

n = 1 gives 1.5 × 1 = 1.5

n = 2 gives 1.5 x 2 = 3

n = 3 gives 1.5 × 3 = 4.5

n = 4 gives 1.5 × 4 = 6

10.

Which sequence can be formed from the given rule for the n^{th} term?.

n^{th} term = 2n - n

n

0, 1, 2, 3 ...

1, 3, 5, 7 ...

1, 2, 3, 4 ...

0, 2, 4, 6 ...

The terms of the sequence are found by first putting n = 1, then n = 2, then n = 3 and finally n = 4 in the rule for the n^{th} term = 2n - n. As follows (do the multiplication first THEN the subtraction):

n = 1 gives 2 x 1 - 1 = 1

n = 2 gives 2 x 2 - 2 = 2

n = 3 gives 3 x 2 - 3 = 3

n = 4 gives 4 x 2 - 4 = 4

n = 1 gives 2 x 1 - 1 = 1

n = 2 gives 2 x 2 - 2 = 2

n = 3 gives 3 x 2 - 3 = 3

n = 4 gives 4 x 2 - 4 = 4

^{th}term = 3n + 2. As follows (do the multiplication first THEN the addition):n = 1 gives 3 × 1 + 2 = 5

n = 2 gives 3 × 2 + 2 = 8

n = 3 gives 3 × 3 + 2 = 11

n = 4 gives 3 × 4 + 2 = 14