AMC12 Sequences & Series 1 — Questions and Answers
Question 1: What is the 10th term of the arithmetic sequence 3, 7, 11, ...?
- 43
- 41
- 37
- 39 (Correct answer)
Correct answer: 39
a_10=3+(10-1)*4=3+36=39.
Question 2: What is the sum of the first 20 positive integers?
- 200
- 190
- 400
- 210 (Correct answer)
Correct answer: 210
S_20=20*21/2=210.
Question 3: What is the common ratio of the geometric sequence 2, 6, 18, ...?
- 4
- 2
- 6
- 3 (Correct answer)
Correct answer: 3
Each term is multiplied by 6/2=3 to get the next, so the common ratio is 3.
Question 4: What is the sum to infinity of 1 + 1/2 + 1/4 + ...?
- 4
- 1
- infinity
- 2 (Correct answer)
Correct answer: 2
S=a/(1-r)=1/(1-1/2)=2.
Question 5: The 5th term of an arithmetic sequence is 17 and the 10th term is 32. What is the common difference?
- 5
- 2
- 4
- 3 (Correct answer)
Correct answer: 3
d=(32-17)/(10-5)=15/5=3.
Question 6: What is the sum of the infinite geometric series 3 + 1 + 1/3 + ...?
- 3
- 4
- 6
- 9/2 (Correct answer)
Correct answer: 9/2
S=3/(1-1/3)=3/(2/3)=9/2.
AMC12 Sequences & Series 1
What is the 10th term of the arithmetic sequence 3, 7, 11, ...?