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.

Read the first 6 Patterns and Sequences flashcards as text

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

    Answer: 17

    The sequence increases by 3 each time; 14 + 3 = 17.

  2. What is the 10th term of the arithmetic sequence 3, 7, 11, 15, ...?

    Answer: 39

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

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

    Answer: 36

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

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

    Answer: 24

    Each term is multiplied by 2: 3, 6, 12, 24, 48.

  5. What is the sum of the first 10 terms of the arithmetic sequence 1, 3, 5, 7, ...?

    Answer: 100

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

  6. In a geometric sequence, the first term is 2 and the common ratio is 3. What is the 4th term?

    Answer: 54

    4th term = 2 × 3^(4−1) = 2 × 27 = 54.

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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