IMO Patterns and Sequences 1 ā Questions and Answers
Question 1: What is the next number in the sequence: 2, 5, 8, 11, 14, ___?
- 15
- 16
- 17 (Correct answer)
- 18
Correct answer: 17
The sequence increases by 3 each time; 14 + 3 = 17.
Question 2: What is the 10th term of the arithmetic sequence 3, 7, 11, 15, ...?
- 38
- 39 (Correct answer)
- 40
- 43
Correct answer: 39
First term a = 3, common difference d = 4; 10th term = 3 + (10ā1) Ć 4 = 3 + 36 = 39.
Question 3: What comes next in the pattern: 1, 4, 9, 16, 25, ___?
- 30
- 34
- 36 (Correct answer)
- 49
Correct answer: 36
These are perfect squares: 1Ā², 2Ā², 3Ā², 4Ā², 5Ā², 6Ā² = 36.
Question 4: Find the missing term: 3, 6, 12, ___, 48
- 18
- 20
- 24 (Correct answer)
- 30
Correct answer: 24
Each term is multiplied by 2: 3, 6, 12, 24, 48.
Question 5: What is the sum of the first 10 terms of the arithmetic sequence 1, 3, 5, 7, ...?
- 90
- 100 (Correct answer)
- 110
- 120
Correct answer: 100
Sum = n/2 Ć (first + last) = 10/2 Ć (1 + 19) = 5 Ć 20 = 100.
Question 6: In a geometric sequence, the first term is 2 and the common ratio is 3. What is the 4th term?
- 18
- 27
- 54 (Correct answer)
- 81
Correct answer: 54
4th term = 2 Ć 3^(4ā1) = 2 Ć 27 = 54.
IMO Patterns and Sequences 1
What is the next number in the sequence: 2, 5, 8, 11, 14, ___?