AQA · Mathematics · 8300
GCSE Maths: Quadratic nth term – Version 2
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Quadratic nth term – Version 2 (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.
17 flashcards · Free to study · No account needed
Study this deck
Preparing your cards…
All questions and answers
Read through the full deck, or practise recalling each answer above.
What is constant in a quadratic sequence?
Show answer
The second difference (the difference between consecutive first differences).
Which of these is a quadratic sequence: 1, 1, 2, 3, 5 / 1, 3, 9, 27 / 1, 5, 11, 19, 29 / 1, 11, 21, 31?
Show answer
1, 5, 11, 19, 29, … — its first differences (4, 6, 8, 10) increase by a constant 2, so the second difference is constant.
In a quadratic sequence, the coefficient of n² equals ? the second difference.
Show answer
half
What is the next term of the quadratic sequence 7, 11, 17, 25, …?
Show answer
35. First differences 4, 6, 8 grow by 2, so the next difference is 10 and 25 + 10 = 35.
What are the first three terms of the sequence with nth term n² − 2n + 8?
Show answer
7, 8, 11 (substitute n = 1, 2, 3).
What is the 10th term of the sequence with nth term 3n² − 8n − 20?
Show answer
200. 3(100) − 80 − 20 = 200.
Which term of the sequence n² − 6n + 7 has the value 23?
Show answer
The 8th term. Solve n² − 6n − 16 = 0 → (n − 8)(n + 2) = 0, and n must be positive.
Find the nth term of the quadratic sequence 4, 10, 18, 28, 40, …
Show answer
n² + 3n. Second difference 2 → n²; subtracting n² leaves 3, 6, 9, 12, 15 = 3n.
Find the nth term of the quadratic sequence 9, 17, 29, 45, 65, …
Show answer
2n² + 2n + 5. Second difference 4 → 2n²; subtracting 2n² leaves 7, 9, 11, 13, 15 = 2n + 5.
Find the nth term of the quadratic sequence 7, 5, 1, −5, …
Show answer
−n² + n + 7. Second difference −2 → −n²; adding n² back gives 8, 9, 10, 11 = n + 7.
What is the 100th term of the quadratic sequence −5, −4, 3, 16, 35, …?
Show answer
29 200. The nth term is 3n² − 8n, so 3(10 000) − 800 = 29 200.
In the sequence n² + 3n, two consecutive terms differ by 38. What are their positions?
Show answer
17 and 18. The difference between term n+1 and term n is 2n + 4, so 2n + 4 = 38 gives n = 17.
For the nth term an² + c, what equation does the 2nd term give?
Show answer
4a + c = (second term), because substituting n = 2 gives a(2)² + c = 4a + c.
For the nth term an² + c, what equation does the 5th term give?
Show answer
25a + c = (fifth term), because substituting n = 5 gives a(5)² + c = 25a + c.
How do you find a and c in an² + c given two terms?
Show answer
Substitute each term's position n to get two simultaneous equations, then subtract them to eliminate c and solve for a.
A sequence has nth term an² + c. Its 2nd term is 16 and 5th term is 163. Find a.
Show answer
a = 7. Subtract 4a + c = 16 from 25a + c = 163 to get 21a = 147.
A sequence has nth term an² + c. Its 2nd term is 16 and 5th term is 163. Find c.
Show answer
c = −12. With a = 7, substitute into 4a + c = 16: 28 + c = 16.
Want to create your own cards? Create a free account. AI generation uses credits.