Lesson D5

D5 Geometric sequences and series Quiz: AQA Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson D5, Geometric sequences and series: 20 multiple choice questions for the AQA Maths (7357), Unit 4: Sequences and series, written with Revision Ninja.

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The 20 questions

  1. What is the nth term of a geometric sequence with first term a and common ratio r?

    • a + (n - 1)r
    • a^r (n - 1)
    • a r^n
    • a r^(n - 1)

  2. What is the sum of the first n terms of a geometric series with first term a and ratio r (r not equal to 1)?

    • n/2 (2a + (n - 1)d)
    • a r^n/(r - 1)
    • a(1 - r^n)/(1 - r)
    • a(1 - r^n)/(1 + r)

  3. For which values of r does a geometric series have a sum to infinity?

    • r > 0
    • |r| < 1
    • |r| > 1
    • r = 1

  4. What is the sum to infinity of a convergent geometric series with first term a and ratio r?

    • a/(1 - r)
    • a/(1 + r)
    • ar/(1 - r)
    • a(1 - r)

  5. What is the 8th term of 3, 6, 12, ...?

    • 192
    • 768
    • 384
    • 256

  6. What is the sum of the first 5 terms of 2, 6, 18, ...?

    • 486
    • 242
    • 240
    • 244

  7. What is the sum to infinity of 8 + 4 + 2 + ...?

    • 4
    • 32
    • 16
    • 8

  8. Does the series 5 - 10 + 20 - ... have a sum to infinity?

    • Yes, with sum 5/3
    • No, since |r| = 2 is not less than 1
    • Yes, with sum 5/(1 + 2)
    • No, since r is negative

  9. A geometric sequence has u_3 = 12 and u_5 = 48, with all terms positive. What is r?

    • 2
    • 4
    • -2
    • 1/2

  10. A geometric series has first term 1 and common ratio 1/3. What is its sum to infinity?

    • 1/3
    • 3/2
    • 3
    • 2/3

  11. A car worth £20000 depreciates by 15% each year. What is its value after 3 years?

    • £15000
    • £12282.50
    • £13600
    • £17000

  12. What is the sum of the first 10 terms of 1 + 2 + 4 + ...?

    • 2047
    • 1023
    • 1024
    • 512

  13. Express the recurring decimal 0.363636... as a fraction.

    • 3/8
    • 9/25
    • 4/11
    • 1/3

  14. What value does the sum 1 + 1/2 + 1/4 + ... approach?

    • 1
    • 2
    • 1/2
    • infinity

  15. A geometric series with ratio 1/4 has sum to infinity 12. What is the first term?

    • 16
    • 12
    • 9
    • 3

  16. A geometric series has partial sums S_n = 3^n - 1. What is its common ratio?

    • 3
    • 1
    • 2
    • 9

  17. For the geometric sequence 1, 2, 4, ..., how many terms are needed for the sum to equal 255?

    • 8
    • 7
    • 9
    • 255

  18. A geometric series has a = 5 and sum to infinity 10. What is r?

    • 1/2
    • 2/3
    • -1/2
    • 1/5

  19. £1000 is invested at 4% compound interest per year. What is the balance after 10 years?

    • £1400.00
    • £1040.00
    • £1480.24
    • £1400.24

  20. The sum to infinity of a geometric series is 4 times its first term. What is r?

    • -3/4
    • 1/4
    • 3/4
    • 1/2

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