Practice Test GeeksIMO - International Mathematics Olympiad Practice Test
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Patterns and Sequences Flashcards

6 cards from real IMO practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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

    Answer: 13, 21

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

  2. Which pattern shows square numbers?

    Answer: 1, 4, 9, 16, 25

    1, 4, 9, 16, 25 are the squares of 1, 2, 3, 4, and 5 respectively.

  3. Find the common ratio in the sequence: 5, 15, 45, 135, ...

    Answer: 3

    Each term is multiplied by 3 to get the next: 5 × 3 = 15, 15 × 3 = 45, etc.

  4. What is the 7th term of the sequence 5, 10, 15, 20, ...?

    Answer: 35

    This is an arithmetic sequence with d = 5; 7th term = 5 + (7−1) × 5 = 5 + 30 = 35.

  5. A sequence is defined by: T(n) = 4n − 1. What is T(6)?

    Answer: 23

    T(6) = 4(6) − 1 = 24 − 1 = 23.

  6. What is the sum of the first 5 terms of the geometric sequence 1, 2, 4, 8, 16?

    Answer: 31

    Sum = 1 + 2 + 4 + 8 + 16 = 31.

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Sources & references

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  1. imo-official.org — Test delivery, eligibility, passing score, test dates, exam format · verified Oct 2026
  2. imo2027.hu — Exam dates, registration deadline · verified Oct 2026