COMC Functions and Sequences 2 — Questions and Answers
Question 1: The 3rd term of a geometric sequence is 12 and the 6th term is 96. What is the common ratio?
- 1.5
- 2 (Correct answer)
- 2.5
- 3
Correct answer: 2
t₆ / t₃ = r³ = 96/12 = 8, so r = 2.
Question 2: The sum of the first n terms of a sequence is Sₙ = 3n² + 2n. What is the 5th term?
- 21
- 25
- 29 (Correct answer)
- 33
Correct answer: 29
a₅ = S₅ − S₄ = (75+10) − (48+8) = 85 − 56 = 29.
Question 3: What is the sum of the infinite geometric series 1 − 1/2 + 1/4 − 1/8 + · · ·?
- 1/3
- 1/2
- 2/3 (Correct answer)
- 3/4
Correct answer: 2/3
The series has first term a = 1 and ratio r = −1/2, so S = 1/(1 − (−1/2)) = 2/3.
Question 4: A sequence satisfies aₙ₊₁ = 2aₙ − 1 with a₁ = 3. What is a₅?
- 17
- 25
- 33 (Correct answer)
- 41
Correct answer: 33
a₂=5, a₃=9, a₄=17, a₅=33.
Question 5: The sum of the first n odd positive integers 1 + 3 + 5 + · · · + (2n−1) equals which expression?
- n(n−1)/2
- n² (Correct answer)
- n(n+1)/2
- 2n−1
Correct answer: n²
This is the classical identity: the sum of the first n odd integers equals n².
Question 6: In an arithmetic sequence, the sum of the 3rd and 7th terms is 26, and the sum of the 4th and 8th terms is 30. What is the common difference?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
(a₄+a₈) − (a₃+a₇) = 2d = 30 − 26 = 4, so d = 2.
Question 7: The Fibonacci sequence is F₁=1, F₂=1, Fₙ=Fₙ₋₁+Fₙ₋₂ for n ≥ 3. What is F₁₀?
- 34
- 44
- 55 (Correct answer)
- 64
Correct answer: 55
The sequence begins 1,1,2,3,5,8,13,21,34,55, so F₁₀ = 55.
COMC Functions and Sequences 2
The 3rd term of a geometric sequence is 12 and the 6th term is 96.
What is the common ratio?