IMO Patterns and Sequences 2 — Questions and Answers
Question 1: What are the next two numbers in the Fibonacci sequence: 1, 1, 2, 3, 5, 8, ___, ___?
- 11, 18
- 12, 20
- 13, 21 (Correct answer)
- 14, 22
Correct answer: 13, 21
Each term is the sum of the two preceding terms: 8 + 5 = 13, then 13 + 8 = 21.
Question 2: Which pattern shows square numbers?
- 2, 4, 6, 8, 10
- 1, 3, 6, 10, 15
- 1, 4, 9, 16, 25 (Correct answer)
- 2, 6, 12, 20, 30
Correct answer: 1, 4, 9, 16, 25
1, 4, 9, 16, 25 are the squares of 1, 2, 3, 4, and 5 respectively.
Question 3: Find the common ratio in the sequence: 5, 15, 45, 135, ...
- 2
- 3 (Correct answer)
- 5
- 10
Correct answer: 3
Each term is multiplied by 3 to get the next: 5 × 3 = 15, 15 × 3 = 45, etc.
Question 4: What is the 7th term of the sequence 5, 10, 15, 20, ...?
- 30
- 35 (Correct answer)
- 40
- 45
Correct answer: 35
This is an arithmetic sequence with d = 5; 7th term = 5 + (7−1) × 5 = 5 + 30 = 35.
Question 5: A sequence is defined by: T(n) = 4n − 1. What is T(6)?
- 21
- 23 (Correct answer)
- 25
- 27
Correct answer: 23
T(6) = 4(6) − 1 = 24 − 1 = 23.
Question 6: What is the sum of the first 5 terms of the geometric sequence 1, 2, 4, 8, 16?
- 25
- 31 (Correct answer)
- 32
- 63
Correct answer: 31
Sum = 1 + 2 + 4 + 8 + 16 = 31.
IMO Patterns and Sequences 2
What are the next two numbers in the Fibonacci sequence: 1, 1, 2, 3, 5, 8, ___, ___?