AQA · Mathematics · 8300
GCSE Maths: Quadratic nth term – Version 1
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Quadratic nth term – Version 1 (Corbettmaths Video 388), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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In a quadratic sequence, the ? differences are constant.
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second
How do you find the coefficient of n² in a quadratic sequence's nth term?
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Halve the constant second difference. E.g. second difference 4 → the nth term starts 2n².
After subtracting the an² part from each term of a quadratic sequence, what remains is a ? sequence.
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linear
What is the next term of the quadratic sequence 7, 11, 17, 25, …?
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35. The differences are 4, 6, 8, so the next difference is 10 and 25 + 10 = 35.
Which is quadratic: 1, 1, 2, 3, 5; 1, 3, 9, 27; 1, 5, 11, 19, 29; or 1, 11, 21, 31?
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1, 5, 11, 19, 29 — its differences 4, 6, 8, 10 have a constant second difference of 2. The others are Fibonacci, geometric and linear.
What is the 6th term of the sequence with nth term 2n² + 3n − 1?
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89. Substitute n = 6: 2(36) + 18 − 1 = 89.
Which term of the sequence n² − 6n + 7 has the value 23?
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The 8th term. Solve n² − 6n + 7 = 23 → n² − 6n − 16 = 0 → (n − 8)(n + 2) = 0, and n must be positive, so n = 8.
What is the nth term of the quadratic sequence 4, 10, 18, 28, 40, …?
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n² + 3n. Second difference 2 → n²; subtracting n² leaves 3, 6, 9, 12, 15 = 3n.
What is the nth term of the quadratic sequence −3, 3, 13, 27, 45, …?
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2n² − 5. Second difference 4 → 2n²; subtracting 2n² leaves −5 every time.
What is the nth term of the quadratic sequence 7, 5, 1, −5, …?
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−n² + n + 7. Second difference −2 → −n²; subtracting −n² (i.e. adding n²) leaves 8, 9, 10, 11 = n + 7.
How can you prove every term of the sequence n² − 8n + 21 is positive?
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Complete the square: n² − 8n + 21 = (n − 4)² + 5. Since (n − 4)² ≥ 0, every term is at least 5, so always positive.
In the sequence n² + 3n, which two consecutive terms differ by 38?
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The 17th and 18th terms. The gap between term n and term n + 1 is 2n + 4, so 2n + 4 = 38 gives n = 17 (terms 340 and 378).
What is the general form of the nth term of a quadratic sequence?
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an² + bn + c, where a ≠ 0.
How do you find a and c in nth term an² + c from two given terms?
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Substitute each n to form two simultaneous equations, then subtract to eliminate c and solve for a.
Nth term is an² + c. What equation does the 5th term give?
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25a + c = (5th term), because 5² = 25.
Nth term is an² + c, 2nd term 16, 5th term 163. Find a and c.
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a = 7, c = −12. From 4a + c = 16 and 25a + c = 163: subtracting gives 21a = 147, so a = 7, then c = 16 − 28 = −12.
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