AQA · Mathematics · 8300
GCSE Maths: Quadratic nth term – Version 3
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Quadratic nth term – Version 3 (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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A quadratic sequence is one whose ? 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 gives 2n².
Which of these is quadratic: 1,1,2,3,5; 1,3,9,27,81; 1,5,11,19,29; 1,11,21,31,41?
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1, 5, 11, 19, 29 — its first differences 4, 6, 8, 10 have a constant second difference of 2. The others are Fibonacci, geometric and linear.
What is the next term of the quadratic sequence 7, 11, 17, 25?
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35. First differences 4, 6, 8 rise by 2 each time, so the next difference is 10.
What is the nth term of the quadratic sequence 4, 10, 18, 28, 40?
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n² + 3n. Second difference 2 gives 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 gives 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 gives −n²; adding n² back leaves 8, 9, 10, 11 = n + 7.
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.
How do you find which term of a quadratic sequence has a given value?
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Set the nth term expression equal to the value, rearrange to a quadratic = 0, solve (e.g. by factorising) and keep the positive integer root.
Which term of the sequence n² − 6n + 7 has the value 23?
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The 8th term. n² − 6n − 16 = 0 factorises to (n − 8)(n + 2) = 0, so n = 8.
In the sequence n² + 3n, which two consecutive terms differ by 38?
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The 17th and 18th terms. The difference between term n+1 and term n is 2n + 4, so 2n + 4 = 38 gives n = 17.
How do you prove every term of 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.
What is the general form of the nth term of a quadratic sequence?
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an² + bn + c, where a ≠ 0.
Given nth term an² + c, what equation does the 2nd term give?
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4a + c = (second term), because substituting n = 2 gives a(2)² + c.
How do you find a and c in an² + c given two terms?
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Substitute each n to get two simultaneous equations, then subtract them to eliminate c and solve for a.
Nth term an² + c: 2nd term 16, 5th term 163. Find a and c.
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a = 7, c = −12. (4a + c = 16 and 25a + c = 163; subtracting gives 21a = 147.)
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