AMC12 Sequences and Series 2 — Questions and Answers
Question 1: Which term of the arithmetic sequence 4, 7, 10, 13, ... is equal to 100?
- 33rd (Correct answer)
- 34th
- 32nd
- 35th
Correct answer: 33rd
4 + (n−1) × 3 = 100 gives 3(n−1) = 96, so n = 33.
Question 2: A ball is dropped from 16 feet and bounces to 3/4 of its height each time. What is the total distance traveled?
- 112 ft (Correct answer)
- 64 ft
- 128 ft
- 100 ft
Correct answer: 112 ft
Total = 16 + 2 × (12)/(1/4) = 16 + 96 = 112 feet.
Question 3: What is ∑(k=1 to 5) k²?
- 55 (Correct answer)
- 45
- 25
- 30
Correct answer: 55
1² + 2² + 3² + 4² + 5² = 1 + 4 + 9 + 16 + 25 = 55.
Question 4: A sequence has aₙ = 2n − 1. What is a₁ + a₂ + ... + a₁₀?
- 100 (Correct answer)
- 55
- 110
- 90
Correct answer: 100
This is the sum of the first 10 odd numbers, which equals 10² = 100.
Question 5: In a geometric series with a₁ = 1 and r = 2, what is a₄?
- 8 (Correct answer)
- 4
- 16
- 12
Correct answer: 8
a₄ = a₁ × r³ = 1 × 2³ = 8.
Question 6: What is the arithmetic mean of 2, 5, 8, 11, 14?
- 8 (Correct answer)
- 7
- 9
- 10
Correct answer: 8
The sum is 40, divided by 5 gives mean = 8; it also equals the middle term of this AP.
AMC12 Sequences and Series 2
Which term of the arithmetic sequence 4, 7, 10, 13, ... is equal to 100?