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!
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the rule for the nth term = -n + 20. As follows:
n = 1 gives -1 + 20 = 19 n = 2 gives -2 + 20 = 18 n = 3 gives -3 + 20 = 17 n = 4 gives -4 + 20 = 16 |
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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 = 2.5n + 22. As follows:
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 |
To find the rule, test each option against the numbers in the sequence. Only one will work:
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 |
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To find the rule, test each option against the numbers in the sequence. Only one will work:
n = 1, and 27 = -1 + 28 n = 2, and 26 = -2 + 28 n = 3, and 25 = -3 + 28 n = 4, and 24 = -4 + 28 |
To find the rule, test each option against the numbers in the sequence. Only one will work:
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! |
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The values are increasing by 17 as the sequence continues:
88 + 17 = 105 105 + 17 = 122 122 = 17 = 139, etc… |
The values are decreasing by 4.5 as the sequence continues:
-22 - 4.5 = -26.5 -26.5 - 4.5 = -31 -31 - 4.5 = -35.5, etc… |
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This one was very tricky, so well done if you got it right.
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… |
The sequence is increasing by 0.5 as it progresses:
5.5 = 0.5 = 6 6 + 0.5 = 6.5 6.5 + 0.5 = 7, etc… |
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