AIME Sequences and Series 1 — Questions and Answers
Question 1: Find the 10th term of the arithmetic sequence 3, 7, 11, 15, …
- 39 (Correct answer)
- 43
- 35
- 41
Correct answer: 39
a_n=3+(n-1)×4; a_10=3+36=39.
Question 2: What is the sum of the first 20 terms of the arithmetic sequence 2, 5, 8, 11, …?
- 610 (Correct answer)
- 590
- 630
- 570
Correct answer: 610
S_20=20/2×(2·2+19·3)=10×(4+57)=10×61=610.
Question 3: Find the common ratio of the geometric sequence 3, 6, 12, 24, …
- 2 (Correct answer)
- 3
- 4
- 6
Correct answer: 2
Each term is doubled: ratio = 6/3 = 2.
Question 4: Find the 6th term of the geometric sequence 2, 6, 18, …
- 486 (Correct answer)
- 162
- 1458
- 324
Correct answer: 486
a_6=2×3^5=2×243=486.
Question 5: What is the sum of the infinite geometric series 4 + 2 + 1 + 1/2 + …?
- 8 (Correct answer)
- 6
- 10
- 12
Correct answer: 8
S=a/(1-r)=4/(1-1/2)=4/(1/2)=8.
Question 6: An arithmetic sequence has first term 5 and common difference -3. Find the sum of the first 10 terms.
- -85 (Correct answer)
- 85
- -95
- 50
Correct answer: -85
S_10=(10/2)(2×5+9×(-3))=5(10-27)=5(-17)=-85.
AIME Sequences and Series 1
Find the 10th term of the arithmetic sequence 3, 7, 11, 15, …