4.5.1 Geometric sequences and series Quiz: Pearson Edexcel Maths, Unit 4

The 20 questions

1. What term is used to describe the constant ratio between consecutive terms in a geometric sequence?

   • Common multiple
   • Common difference
   • Common factor
   • Common ratio

2. Which letter is standard notation for the common ratio of a geometric sequence?

   • a
   • d
   • n
   • r

3. What is the standard formula for the nth term of a geometric sequence?

   • ar^(n-1)
   • a + (n-1)d
   • ar^n
   • a + nr

4. What does the letter a represent in the standard geometric sequence formula?

   • First term
   • Common ratio
   • Number of terms
   • Last term

5. Under what condition does an infinite geometric series converge to a sum to infinity?

   • r > 1
   • r = 1
   • mod r > 1
   • mod r < 1

6. What is the formula for the sum to infinity of a convergent geometric series?

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

7. What type of sequence is 3, 6, 12, 24, ...?

   • Arithmetic
   • Quadratic
   • Periodic
   • Geometric

8. What is the formula for the sum of the first n terms of a geometric series?

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

9. Find the 4th term of a geometric sequence where a = 2 and r = 3.

   • 162
   • 18
   • 54
   • 24

10. What is the common ratio of the geometric sequence 8, 4, 2, 1, ...?

    • 0.5
    • -2
    • 2
    • 0.25

11. What is the second term of a geometric sequence if a = 5 and the third term is 45?

    • 25
    • 135
    • 15
    • 9

12. If the first term is 3 and the common ratio is -2, what is the third term?

    • -12
    • -18
    • 18
    • 12

13. Which of the following describes a geometric sequence whose terms alternate in sign?

    • r equals 0
    • r equals 1
    • Negative r
    • Positive r

14. What is the exact value of the sum to infinity of 6 + 2 + 2/3 + ...?

    • 8
    • 4.5
    • 18
    • 9

15. If r = 1 for a geometric series with a = 4, what is the sum of the first 10 terms?

    • 41
    • 4
    • 0
    • 40

16. What must be true for a geometric sequence to be strictly increasing with positive terms?

    • a > 0 and r < 0
    • a < 0 and r > 1
    • a > 0 and 0 < r < 1
    • a > 0 and r > 1

17. If log(a), log(ar), and log(ar^2) are formed, what type of sequence are they?

    • Fibonacci
    • Arithmetic
    • Quadratic
    • Geometric

18. What is the common ratio if the 3rd term is 27 and the 1st term is 3?

    • 24
    • 81
    • 3
    • 9

19. Which logarithmic method is often used to find an unknown n in a geometric inequality?

    • Logarithms
    • Factorisation
    • Integration
    • Differentiation

20. What is the 5th term of the geometric sequence starting with 2 and having common ratio 2?

    • 32
    • 16
    • 64
    • 10

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