2.22 nth terms of quadratic sequences Quiz: AQA Further Maths, Unit 2

The 20 questions

1. What property is always true for the second differences of a quadratic sequence?

   • They form a linear sequence
   • They are zero
   • They are constant
   • They double each time

2. What is the general form of the nth term of a quadratic sequence?

   • an^2 + bn + c
   • an + b
   • a^n + b
   • an^3 + bn + c

3. What is the second difference of the sequence 3, 9, 19, 33, ...?

   • 2
   • 10
   • 6
   • 4

4. For a quadratic sequence with second difference 6, what is the coefficient of n^2?

   • 1/2
   • 3
   • 12
   • 6

5. What is the nth term of the sequence 4, 7, 12, 19, ...?

   • n^2 + 2n + 1
   • 2n^2 + 1
   • n^2 + 3
   • n^2 + n + 2

6. What is the nth term of the sequence 5, 12, 23, 38, ...?

   • 2n^2 + 3n
   • 2n^2 + n + 5
   • 4n^2 + n + 2
   • 2n^2 + n + 2

7. What is the nth term of the sequence 6, 8, 6, 0, ...?

   • −2n^2 + 8n
   • −2n^2 + 6n
   • 2n^2 − 8n + 6
   • −2n^2 + 8n + 6

8. For u_n = n^2 − 5n + 4, which term has the value 0 (the smallest such n)?

   • The 4th term
   • The 5th term
   • The 1st term
   • The 2nd term

9. What is the 6th term of the sequence with nth term n^2 − 3n?

   • 18
   • 24
   • 12
   • 36

10. For u_n = 2n^2 + 1, what is u_10 − u_9?

    • 200
    • 19
    • 42
    • 38

11. What is the nth term of the sequence 3, 5, 9, 15, ...?

    • n^2 − n + 2
    • n^2 − n + 3
    • n^2 + n + 1
    • 2n^2 − n + 3

12. What is the 20th term of the sequence with nth term n^2 + 2n?

    • 450
    • 420
    • 400
    • 440

13. Which term of the sequence n^2 + 3n is equal to 40?

    • 8th
    • 40th
    • 4th
    • 5th

14. For the quadratic sequence 10, 16, 18, 16, ..., which term has a value of 0?

    • 5th term
    • 7th term
    • 8th term
    • 6th term

15. What is the nth term of the sequence 1, 6, 15, ...?

    • 2n^2 + n − 2
    • 2n^2 − n
    • n^2 − n
    • 2n^2 − 3n + 2

16. What is the nth term of the sequence 4, 10, 20, 34, ...?

    • 2n^2 + 2n
    • 2n^2 + 2
    • 2n^2 + n + 1
    • 4n^2 + 2

17. For u_n = n^2 + kn, u_3 = 21. What is k?

    • 6
    • 12
    • 3
    • 4

18. For u_n = 2n^2 − 3n + 1, which term has the value 36?

    • The 4th term
    • The 18th term
    • The 5th term
    • The 6th term

19. For u_n = (n + 1)(n + 2), how many terms are less than 100?

    • 10
    • 7
    • 9
    • 8

20. A quadratic sequence starts 2, 7, 16, 29, ... What is its nth term?

    • 2n^2 + n + 1
    • 2n^2 − n + 1
    • 4n^2 − n + 1
    • 2n^2 − n − 1

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