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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!
27, 26, 25, 24, …
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…
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
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
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
-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!
-22, -26.5, X, -35.5, …
-22 - 4.5 = -26.5
-26.5 - 4.5 = -31
-31 - 4.5 = -35.5, etc…
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
5.5, 6, X, 7, …
5.5 = 0.5 = 6
6 + 0.5 = 6.5
6.5 + 0.5 = 7, etc…
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n = 1, and 27 = -1 + 28
n = 2, and 26 = -2 + 28
n = 3, and 25 = -3 + 28
n = 4, and 24 = -4 + 28