IMO Patterns and Sequences 2

Question 1

What are the next two numbers in the Fibonacci sequence: 1, 1, 2, 3, 5, 8, ___, ___?

Accepted Answer

13, 21

Answer

Each term is the sum of the two preceding terms: 8 + 5 = 13, then 13 + 8 = 21.

Question 2

Which pattern shows square numbers?

Accepted Answer

1, 4, 9, 16, 25

Answer

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, ...

Accepted Answer

3

Answer

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, ...?

Accepted Answer

35

Answer

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)?

Accepted Answer

23

Answer

T(6) = 4(6) − 1 = 24 − 1 = 23.

IMO - International Mathematics Olympiad Practice Test