A number 5 on a red background
If the nth term = 5n, simply multiply n by 5.

Number Sequences 2 (Medium)

In the previous Eleven Plus maths quiz we asked you to create number sequences by following certain rules about the nth 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 nth 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 nth term?.
nth term = 3n + 7
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 nth 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
2.
Which sequence can be formed from the given rule for the nth term?.
nth term = -4n
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 nth 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
3.
Which sequence can be formed from the given rule for the nth term?.
nth term = 9n – 5
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 nth 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
4.
Which sequence can be formed from the given rule for the nth term?.
nth term = 12n
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 nth 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
5.
Which sequence can be formed from the given rule for the nth term?.
nth term = 3n + 10
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 nth 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
6.
Which sequence can be formed from the given rule for the nth term?.
nth term = -n + 3
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 nth 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
7.
Which sequence can be formed from the given rule for the nth term?.
nth term = n3
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 nth term = n3. As follows:
n = 1 gives 13 = 1
n = 2 gives 23 = 8
n = 3 gives 33 = 27
n = 4 gives 43 = 64
8.
Which sequence can be formed from the given rule for the nth term?.
nth term = 2n - 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 nth 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
9.
Which sequence can be formed from the given rule for the nth term?.
nth term = 3n + 2
5, 8, 11, 14 ...
7, 9, 11, 14 ...
5, 9, 11, 14
5, 8, 11, 15
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 nth 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
10.
Which sequence can be formed from the given rule for the nth term?.
nth term = 1.5n
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 nth 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
Author:  Frank Evans

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