10 questions · Form 4 Additional Mathematics Bab 5: Progressions
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Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. The first term of an AP is -8 and the last term is 52. If the sum of all terms is 220, find the number of terms n.
Answer: A
S_n = (n2)[a + l] => 220 = (n2)[-8 + 52] => 220 = (n2)[44] => 220 = 22n => n = 10.
2. The 3rd term of an AP is 10 and the 8th term is 25. Find the common difference d.
Answer: A
T₃ = a + 2d = 10, T₈ = a + 7d = 25. Subtracting equations: 5d = 15 => d = 3.
3. Three consecutive terms of an arithmetic progression are x - 1, x + 3, and 3x + 1. Find the value of x.
Answer: A
In an AP, (T₂ - T₁) = (T₃ - T₂) => (x + 3) - (x - 1) = (3x + 1) - (x + 3) => 4 = 2x - 2 => 2x = 6 => x = 3.
4. Find the sum to infinity of the geometric progression: 12, 4, 43, 49, ...
Answer: A
a = 12, r = 412 = 13. S_∞ = a1 - r = 12 / (1 - 13) = 12 / (23) = 18.
5. Find the 7th term of the geometric progression: 2, 6, 18, 54, ...
Answer: A
a = 2, r = 3. T₇ = a r⁶ = 2 × 3⁶ = 2 × 729 = 1458.
6. The first term of a GP is 5 and the common ratio is 2. Which term of the progression is equal to 320?
Answer: A
T_n = a r^(n-1) => 5(2)^(n-1) = 320 => 2^(n-1) = 64 => 2^(n-1) = 2⁶ => n - 1 = 6 => n = 7.
7. Calculate the sum of the first 20 terms of the arithmetic progression: 2, 5, 8, 11, ...
Answer: A
a = 2, d = 3, n = 20. S₂₀ = (202)[2(2) + (20 - 1)(3)] = 10[4 + 57] = 10[61] = 610.
8. In a geometric progression, T₂ = 12 and T₅ = 324. Find the first term a.
Answer: A
T₂ = ar = 12, T₅ = ar⁴ = 324. Divide T₅ by T₂: r³ = 32412 = 27 => r = 3. Since ar = 12 => a(3) = 12 => a = 4.
9. Find the common ratio r of the geometric progression: 162, -54, 18, -6, ...
Answer: A
r = T₂ / T₁ = -54162 = -13.
10. If k + 2, 2k, and 3k + 6 are three consecutive terms of a geometric progression with positive terms, find the value of k.
Answer: A
In a GP, T₂ / T₁ = T₃ / T₂ => 2kk + 2 = 3k + 62k => (2k)² = (k + 2)(3k + 6) => 4k² = 3k² + 12k + 12 => k² - 12k - 12 = 0 => (k - 6)(k + 2) = 0... For k = 6: terms are 8, 12, 24 (r = 1.5).