The Nth Term of a Quadratic Sequence worksheet
10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.
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3 marks
Here are the first four terms of a quadratic sequence.
\(1,\ 18,\ 45,\ 82\)
(a)Work out the next two terms of the sequence.
(b)State the second difference of the sequence.
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2 marks
The \(n\)th term of a quadratic sequence is
\(3n^2 + 7n - 9\)
Write down the first three terms of the sequence.
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3 marks
Five terms of a quadratic sequence are shown below. One of them is missing.
\(19,\ 37,\ ?,\ 103,\ 151\)
Work out the missing term.
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2 marks
Here are the first five terms of each of three sequences.
A \({sa:mathlist}\)
B \({sb:mathlist}\)
C \({sc:mathlist}\)
Exactly one of them is a quadratic sequence.
Write down the letter of the quadratic sequence, and explain how you can tell.
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3 marks
The table gives the first five terms of a quadratic sequence.
Position 1 2 3 4 5 Term 5 16 33 56 85 Find an expression, in terms of \(n\), for the \(n\)th term of the sequence.
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5 marks
A quadratic sequence begins
\(7,\ 19,\ 35,\ 55,\ 79,\ \dots\)
(a)Find an expression, in terms of \(n\), for the \(n\)th term of the sequence.
(b)Work out the 12th term of the sequence.
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3 marks
The \(n\)th term of a quadratic sequence is
\(n^2 + 3n - 5\)
One term of the sequence is equal to \(83\).
Find the position of that term in the sequence.
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3 marks
The \(n\)th term of a quadratic sequence is \(an^2 + bn + c\).
The second difference of the sequence is \(2\).
The first term is \(18\) and the second term is \(23\).
(a)Write down the value of \(a\).
(b)Work out the value of \(b\) and the value of \(c\).
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3 marks
The \(n\)th term of a quadratic sequence is
\(n^2 + 4n + 9\)
Work out the first term of the sequence that is greater than \(33\).
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3 marks
A quadratic sequence begins
\(0,\ 7,\ 18,\ 33,\ \dots\)
Is 133 a term of this sequence?
You must explain your answer.
Answers
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(a) \(129\) and \(186\)
(b) \(10\) - \(1,\ 17,\ 39\)
- \(65\)
- \({letter}\). Its second differences are all \({sd}\) — equal to each other and not zero, which is what makes a sequence quadratic.
- \(3n^2 + 2n \)
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(a) \(2n^2 + 6n - 1\)
(b) \(359\) - \(n = 8\)
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(a) \(a = 1\)
(b) \(b = 2\) and \(c = 15\) - \(41\)
- Yes — the 8th term is 133 and the 9th term is 168, so 133 is a term of the sequence.