IMO Practice Test — Number Patterns
6 Questions • 10 min • Olympiad level
10:00
Question 1 of 6
hard
Find the next term: 2, 5, 10, 17, 26, ___
37
33
30
35
Explanation: Differences: +3, +5, +7, +9, +11. Next difference is +11. 26 + 11 = 37.
Question 2 of 6
hard
What is the missing term? 1, 3, 6, 10, ___, 21
12
14
15
16
Explanation: Differences: +2, +3, +4, +5, +6. Missing term: 10+5=15. Check: 15+6=21.
Question 3 of 6
hard
Input 1 gives 1, input 2 gives 4, input 3 gives 9, input 4 gives 16. What rule is being followed?
add input to previous
multiply by 4
multiply input by itself
add 3 each time
Explanation: 1x1=1, 2x2=4, 3x3=9, 4x4=16. The rule is to square the input (multiply by itself).
Question 4 of 6
hard
A pattern starts at 100 and each term is half the previous. What is the 4th term?
25
12.5
50
20
Explanation: 100, 50, 25, 12.5. The 4th term is 12.5 (dividing by 2 each time).
Question 5 of 6
hard
Find the next term: 5, 7, 11, 17, 25, ___
35
30
33
40
Explanation: Differences: +2, +4, +6, +8, +10. Next difference is +10. 25 + 10 = 35.
Question 6 of 6
hard
Which number does NOT belong in this pattern? 3, 6, 12, 24, 48, 50
50
48
24
6
Explanation: The rule is x2: 3,6,12,24,48,96. 50 does not follow the rule (it should be 96 after 48).