2.20 Using nth terms of sequences Limiting value of a sequence as n → ∞ Quiz: AQA Further Maths, Unit 2

The 20 questions

1. The nth term of a sequence is 3n − 1. What is the 4th term?

   • 8
   • 11
   • 12
   • 9

2. What is the limit of 1/n as n → ∞?

   • −1
   • 1
   • 0
   • ∞

3. What is the limit of 3 + 1/n as n → ∞?

   • ∞
   • 4
   • 3
   • 0

4. For the sequence with nth term n^2, what is the difference between the 10th and 5th terms?

   • 125
   • 5
   • 25
   • 75

5. Which sequence has a limit of ∞ as n → ∞?

   • n^2
   • 1/n
   • 5
   • (−1)^n

6. What is the 1st term of the sequence with nth term 4n − 7?

   • 4
   • 1
   • −7
   • −3

7. For u_n = 5 − 1/n, what is u_10 − u_2?

   • 0.4
   • 0.5
   • −0.4
   • 0.6

8. What is the limit of (2n + 1)/(n + 3) as n → ∞?

   • 2
   • 0
   • 1
   • ∞

9. What is the limit of 3n^2/(n^2 + 5) as n → ∞?

   • 3
   • ∞
   • 0
   • 3/5

10. What is the limit of (4n + 1)/(2n − 3) as n → ∞?

    • 4
    • 0
    • 2
    • 1/2

11. In the sequence with nth term 5n − 7, which term has the value 48?

    • 12
    • 11
    • 9
    • 10

12. What is the nth term of the sequence 3, 6, 9, 12, ...? Which term equals 99?

    • 99
    • 33
    • 30
    • 32

13. What is the limit of (n + 2)/(3n) as n → ∞?

    • 0
    • 1
    • 3
    • 1/3

14. What is the behaviour of the terms of the sequence 2 − 3n as n → ∞?

    • They tend to 2.
    • They tend to −∞.
    • They tend to ∞.
    • They tend to 0.

15. What is the limiting value of the sequence with nth term 2n / (n + 4) as n → ∞?

    • 4
    • 2
    • 1
    • 0

16. What is the limit of (n^2 − 1)/(n + 1) as n → ∞?

    • ∞
    • −1
    • 0
    • 1

17. What is the limit of (2n^2 + 3n)/(n^2 − 4) as n → ∞?

    • 0
    • ∞
    • 3
    • 2

18. The nth term is 100/n. What is the smallest n for which the term is less than 0.5?

    • 250
    • 199
    • 200
    • 201

19. What is the limit of (4n + 2)/n as n → ∞?

    • 2
    • 6
    • 4
    • 0

20. Which sequence does NOT have a limit as n → ∞?

    • (−1)^n
    • n/(n + 1)
    • 1/n
    • 2 + 1/n

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