The numbers 1, 2 1nd 3 on purple background
If a number sequence increases by one each time, the rule for the nth term is n + 1.

Number Sequences 2 (Difficult)

Welcome to the second of our difficult Eleven Plus maths quizzes on Number Sequences. By now you should be a dab hand at finding the missing values in a series – if not, this quiz will give you plenty of opportunity to practice.

There are two ways to tackle these kinds of problems. The first is to attempt to find the rule for the nth term. The second is to try to work out how the series of numbers is progressing. For example, look at this sequence:

4, 5, 6, 7 …

Obviously, these numbers are increasing by one each time. The rule for the nth term here is n + 1. Simple isn’t it?

1.
Find the missing term.
-19, 4, 27, X, ...
50
40
60
70
The next term is got from the previous term by adding 23, e.g. -19 + 23 = 4 and so on
2.
Find the missing term.
3, 9, 15, 21, X, 33, ...
23
25
27
29
The rule for the nth term = 6n - 3. Put in the values of 1, 2, 3, 4, ... in turn and see for yourself how the sequence is produced
3.
Find the missing term.
0.2, 2.4, 28.8, X, ...
57.9
123.4
288
345.6
The next term is got from the previous term by multiplying by 12, e.g. 0.2 x 12 = 2.4 and so on. You might need to use your calculator for this one!
4.
Find the missing term.
32, 131, X, 329, ...
180
210
240
230
The next term is got from the previous term by adding 99, e.g. 32 + 99 = 131 and so on
5.
Find the missing term.
-2, 2, 6, 10, X, ...
11
12
13
14
The rule for the nth term = 5n - (n + 2). Put in the values of 1, 2, 3, 4, ... in turn and see for yourself how the sequence is produced
6.
Find the missing term.
0, 1.2, 1.44, X, ...
1.88
1.728
1.96
2.223
The next term is got from the previous term by multiplying by 1.2, e.g. 1.2 x 1.2 = 1.44 and so on.
Sometimes it is necessary to use your calculator!
7.
Find the missing term.
1,000, 250, X, 15.625 ...
125
104
62.5
48.4
The next term is got from the previous term by dividing by 4, e.g. 1,000 ÷ 4 = 250 and so on
8.
Find the missing term.
-84, -42, -21, X, ...
-10.5
-14
-7
-8.5
The next term is got from the previous term by dividing by 2, e.g. -84 ÷ 2 = -42 and so on
9.
Find the missing term.
22, 8, X, -20, ...
-2
-6
2
6
The next term is got from the previous term by subtracting 14, e.g. 22 – 14 = 8 and so on
10.
Find the missing term.
-2, 2, 6, X, ...
14
12
10
8
The rule for the nth term = 3n + (n - 2). Put in the values of 1, 2, 3, 4, ... in turn and see for yourself how the sequence is produced
Author:  Frank Evans

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