High School

Complete the number pattern.

1) 91, 88, 85, 82, 79, 76

2) 5, 20, 80, 320, __, __

3) 200000, 20000, 2000, 200, 20, 2

4) 26, 13, __, __, 10, 5, __, 8, 4, 2, 1

5) 6, 3, 10, __, __, __, 4, 2, 2

6) 3, 12, 48, 192, __

Answer :

To complete the number patterns given in the question, let's analyze each sequence step by step.

  1. 91, 88, 85, 82, 79, 76

    This pattern is decreasing by 3 each time. We can extend this sequence by subtracting 3 from the last number:

    [tex]76 - 3 = 73[/tex]

    So the next number is 73.

  2. 5, 20, 80, 320, __, __

    In this pattern, each number is being multiplied by 4 to get the next number:

    [tex]320 \times 4 = 1280[/tex]
    [tex]1280 \times 4 = 5120[/tex]

    So the next two numbers are 1280 and 5120.

  3. 200000, 20000, 2000, 200, 20, 2

    This sequence is decreasing by dividing each number by 10:

    [tex]20 \div 10 = 2[/tex]

    The numbers are decreasing correctly according to the pattern, so the next number is already provided, which is 2.

  4. 26, 13, __, __, 10, 5, __, 8, 4, 2, 1

    Observing the pattern, each number is half of the previous one or subtracted by a certain number. Starting at 26:

    [tex]26 \div 2 = 13[/tex]
    [tex]13 - 3 = 10[/tex]
    [tex]10 \div 2 = 5[/tex]
    [tex]5 + 3 = 8[/tex]
    [tex]8 \div 2 = 4[/tex]
    [tex]4 \div 2 = 2[/tex]
    [tex]2 - 1 = 1[/tex]

    Filling the missing values, we get 10, 5, and 1.

  5. 6, 3, 10, __, __, __, 4, 2, 2

    The sequence does not follow a clear arithmetic or geometric progression, so there might be a pattern involving multiple operations or it could be a typo mistake.

    As per numbers [tex]6, 3, 10[/tex], it could likely be [tex]10/2[/tex]. Hence clarification is needed for a definitive completion.

  6. 3, 12, 48, 192, __

    In this sequence, each term is multiplied by 4 from the previous term:

    [tex]192 \times 4 = 768[/tex]

    So the next number is 768.

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