IMO Practice Test — Patterns & Sequences
6 Questions • 15 min • Olympiad level
15:00
Question 1 of 6
Find the sum of the first 20 terms of the sequence: 5, 9, 13, 17, ...
820
860
840
880
Explanation: a₁=5,d=4; a₂₀=5+19×4=81; Sum = n/2(a₁+aₙ)=20/2×(5+81)=10×86=860
Question 2 of 6
In a geometric sequence, the 3rd term is 18 and the 6th term is 486. Find the first term.
2
3
4
6
Explanation: a₃=ar²=18; a₆=ar⁵=486; divide: (ar⁵)/(ar²)=r³=486/18=27; r=3; a×9=18 → a=2
Question 3 of 6
A pattern of tiles forms a rectangle: Figure 1: 1×2=2 tiles, Figure 2: 2×3=6 tiles, Figure 3: 3×4=12 tiles. How many tiles in Figure 12?
132
144
156
168
Explanation: Formula: n×(n+1); Figure 12: 12×13=156
Question 4 of 6
Which term of the arithmetic sequence 70, 63, 56, ... equals -14?
10th
11th
12th
13th
Explanation: a₁=70,d=-7; 70+(n-1)(-7)=-14; 70-7n+7=-14; 77-7n=-14; -7n=-91; n=13
Question 5 of 6
A ball bounces to 80% of its previous height. If dropped from 2 metres, what height after the 5th bounce? (in cm)
32.8 cm
65.5 cm
81.9 cm
102.4 cm
Explanation: a₁=200cm,r=0.8; a₆=200×(0.8)⁵=200×0.32768=65.536 ≈65.5 cm
Question 6 of 6
The pattern shows: Figure 1: 5 matchsticks, Figure 2: 9 matchsticks, Figure 3: 13 matchsticks. Which figure uses 101 matchsticks?
24th
25th
26th
27th
Explanation: a₁=5,d=4; aₙ=5+(n-1)4=101; 4n-4=96; 4n=100; n=25