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Quiz Chapter 5: Progressions

10 questions · Form 4 Additional Mathematics Bab 5: Progressions

10 questions · plays in fullscreen

Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. The sum to infinity of a GP is 27 and its common ratio is 13. Find the first term a.

  1. 18
  2. 9
  3. 81
  4. 12
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Answer: A

S_∞ = a1 - r => 27 = a / (1 - 13) => 27 = a / (23) => a = 27 × (23) = 18.

2. Find the common difference of the AP whose n-th term is T_n = 5 - 3n.

  1. -3
  2. 3
  3. 5
  4. -2
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Answer: A

T₁ = 5 - 3(1) = 2. T₂ = 5 - 3(2) = -1. d = T₂ - T₁ = -1 - 2 = -3.

3. Under what condition does a geometric progression have a sum to infinity (S_∞)?

  1. -1 < r < 1
  2. r > 1
  3. r < -1
  4. r = 1
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Answer: A

A infinite geometric progression converges to a finite sum if and only if |r| < 1, which means -1 < r < 1.

4. Find the sum to infinity of the geometric progression: 12, 4, 43, 49, ...

  1. 18
  2. 16
  3. 24
  4. 12
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Answer: A

a = 12, r = 412 = 13. S_∞ = a1 - r = 12 / (1 - 13) = 12 / (23) = 18.

5. The 3rd term of an AP is 10 and the 8th term is 25. Find the common difference d.

  1. 3
  2. 4
  3. 5
  4. 2
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Answer: A

T₃ = a + 2d = 10, T₈ = a + 7d = 25. Subtracting equations: 5d = 15 => d = 3.

6. Find the common ratio r of the geometric progression: 162, -54, 18, -6, ...

  1. -13
  2. 13
  3. -3
  4. 3
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Answer: A

r = T₂ / T₁ = -54162 = -13.

7. Express the recurring decimal 0.4444... as a fraction in its simplest form using sum to infinity.

  1. 49
  2. 410
  3. 25
  4. 411
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Answer: A

0.4444... = 0.4 + 0.04 + 0.004 + ... which is a GP with a = 0.4, r = 0.1. S_∞ = 0.41 - 0.1 = 0.40.9 = 49.

8. An employee's starting annual salary is RM 36 000 with an annual increment of RM 2 400. Calculate total salary earned after 10 years.

  1. RM 468 000
  2. RM 432 000
  3. RM 504 000
  4. RM 384 000
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Answer: A

AP with a = 36000, d = 2400, n = 10. S₁₀ = (102)[2(36000) + 9(2400)] = 5[72000 + 21600] = 5[93600] = RM 468 000.

9. Three consecutive terms of an arithmetic progression are x - 1, x + 3, and 3x + 1. Find the value of x.

  1. 4
  2. 3
  3. 5
  4. 2
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Answer: A

In an AP, (T₂ - T₁) = (T₃ - T₂) => (x + 3) - (x - 1) = (3x + 1) - (x + 3) => 4 = 2x - 2 => 2x = 6 => x = 3.

10. Calculate the sum of the first 20 terms of the arithmetic progression: 2, 5, 8, 11, ...

  1. 610
  2. 590
  3. 620
  4. 580
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Answer: A

a = 2, d = 3, n = 20. S₂₀ = (202)[2(2) + (20 - 1)(3)] = 10[4 + 57] = 10[61] = 610.

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