AMC12 Sequences and Series 1 — Questions and Answers
Question 1: What is the 10th term of the arithmetic sequence 3, 7, 11, 15, ...?
- 39 (Correct answer)
- 43
- 35
- 47
Correct answer: 39
The common difference is 4, so a₁₀ = 3 + 9 × 4 = 3 + 36 = 39.
Question 2: What is the sum of the first 100 positive integers?
- 5050 (Correct answer)
- 5000
- 4950
- 10100
Correct answer: 5050
Sum = n(n+1)/2 = 100 × 101/2 = 5050, as computed by Gauss.
Question 3: A geometric sequence has first term 2 and common ratio 3. What is the 5th term?
- 162 (Correct answer)
- 486
- 54
- 243
Correct answer: 162
a₅ = a₁ × r^(n−1) = 2 × 3⁴ = 2 × 81 = 162.
Question 4: What is the sum of the infinite geometric series 1 + 1/2 + 1/4 + 1/8 + ...?
- 2 (Correct answer)
- 4
- 1
- 3/2
Correct answer: 2
S∞ = a/(1−r) = 1/(1−1/2) = 2.
Question 5: In the Fibonacci sequence 1, 1, 2, 3, 5, 8, ..., what is the 8th term?
- 21 (Correct answer)
- 13
- 34
- 18
Correct answer: 21
Continuing the Fibonacci sequence: the 8th term is 21.
Question 6: The sum of the first n terms is Sₙ = 2n² + 3n. What is the first term a₁?
- 5 (Correct answer)
- 2
- 3
- 7
Correct answer: 5
a₁ = S₁ = 2(1)² + 3(1) = 5.
AMC12 Sequences and Series 1
What is the 10th term of the arithmetic sequence 3, 7, 11, 15, ...?