IMO Patterns and Sequences

Question 1

What is the next number in the sequence: 2, 5, 8, 11, 14, ___?

Accepted Answer

17

Answer

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, ...?

Accepted Answer

39

Answer

First term a = 3, common difference d = 4; 10th term = 3 + (10−1) × 4 = 3 + 36 = 39.

Question 3

What comes next in the pattern: 1, 4, 9, 16, 25, ___?

Accepted Answer

36

Answer

These are perfect squares: 1², 2², 3², 4², 5², 6² = 36.

Question 4

Find the missing term: 3, 6, 12, ___, 48

Accepted Answer

24

Answer

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, ...?

Accepted Answer

100

Answer

Sum = n/2 × (first + last) = 10/2 × (1 + 19) = 5 × 20 = 100.

IMO - International Mathematics Olympiad Practice Test