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Number Sequences 3 (Difficult)
This is the third of our Difficult Eleven Plus maths quizzes on Number Sequences. In the first two we asked you to find the missing term in a series. This quiz is more of a mixed bag. You’ll also be asked to find the rule for the nth term which governs the sequence, and to create a sequence when you are given the rule.
In some number sequences the rules are very obvious. They might be increasing or decreasing by a certain amount each time. Others can be trickier, such as the nth term squared or cubed. There are two ways to master number sequences: trial and error (try all the potential answers out for size – only one of them will work) and practise!
If you haven’t already played our previous quizzes on number sequences, then please go back and give them a try. The things you’ll learn by playing them will help you out, not just in this quiz, but in your exams when they come along. Practise makes perfect!
-22, -26.5, X, -35.5, …
nth term = 4n - 17
n = 1 gives (4 x 1) - 17 = -13
n = 2 gives (4 x 2) - 17 = -9
n = 3 gives (4 x 3) - 17 = -5
n = 4 gives (4 x 4) - 17 = -1
nth term = -n + 20
n = 1 gives -1 + 20 = 19
n = 2 gives -2 + 20 = 18
n = 3 gives -3 + 20 = 17
n = 4 gives -4 + 20 = 16
-1, -2, -3, -4, …
n = 1, and -1 = 1 - (2 x 1)
n = 2, and -2 = 2 - (2 x 2)
n = 3, and -3 = 3 - (2 x 3)
n = 4, and -4 = 4 - (2 x 4)
Of course, -n would work too, but that wasn’t one of the options!
27, 26, 25, 24, …
n = 1, and 27 = -1 + 28
n = 2, and 26 = -2 + 28
n = 3, and 25 = -3 + 28
n = 4, and 24 = -4 + 28
5.5, 6, X, 7, …
5.5 = 0.5 = 6
6 + 0.5 = 6.5
6.5 + 0.5 = 7, etc…
nth term = 2.5n + 22
n = 1 gives (2.5 x 1) + 22 = 24.5
n = 2 gives (2.5 x 2) + 22 = 27
n = 3 gives (2.5 x 3) + 22 = 29.5
n = 4 gives (2.5 x 4) + 22 = 32
8, 12, 16, 20, …
n = 1, and 8 = (4 x 1) + 4
n = 2, and 12 = (4 x 2) + 4
n = 3, and 16 = (4 x 3) + 4
n = 4, and 20 = (4 x 4) + 4
0.5, 2, 4.5, X, 12.5, 18, …
The rule for this sequence is the nth term = n2 ÷ 2:
12 ÷ 2 = 0.5
22 ÷ 2 = 2
32 ÷ 2 = 4.5
42 ÷ 2 = 8
52 ÷ 2 = 12.5
62 ÷ 2 = 18, etc…
88, X , 122, 139, …
88 + 17 = 105
105 + 17 = 122
122 = 17 = 139, etc…
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-22 - 4.5 = -26.5
-26.5 - 4.5 = -31
-31 - 4.5 = -35.5, etc…