Number series and rule selection: Practice 1

10 original teaching questions with answers and explanations.

Instructions for this set

Use the rule family explicitly stated in each question. Check the rule against all listed transitions. No claim is made that an unrestricted finite sequence has only one continuation.

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  1. 1. Continue by adding the same amount: 13, 20, 27, 34, ?
    1. 42
    2. 39
    3. 40
    4. 41

    Reference: q-18bc661e-54 · Report this question

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    Answer: D. 41

    The constant difference is seven. Add seven to 34 to get 41.
  2. 2. Continue by multiplying by the same factor: 3, 12, 48, 192, ?
    1. 768
    2. 960
    3. 384
    4. 576

    Reference: q-a879b527-62 · Report this question

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    Answer: A. 768

    Every term is four times the previous one. 192 times four = 768.
  3. 3. Continue using successive differences 2, 4, 6, then 8: 5, 7, 11, 17, ?
    1. 24
    2. 25
    3. 27
    4. 23

    Reference: q-bf8e4557-71 · Report this question

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    Answer: B. 25

    The next difference is eight. Add eight to 17 to get 25.
  4. 4. Continue the two interleaved arithmetic sequences: 2, 30, 5, 25, 8, 20, ?
    1. 15
    2. 10
    3. 11
    4. 12

    Reference: q-f2e4431e-74 · Report this question

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    Answer: C. 11

    Odd positions are 2, 5, 8, 11, increasing by three. Even positions are 30, 25, 20, decreasing by five. The next term is at an odd position, so it is 11.
  5. 5. Continue by multiplying by three and subtracting two: 2, 4, 10, 28, ?
    1. 84
    2. 78
    3. 80
    4. 82

    Reference: q-141d46a1-70 · Report this question

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    Answer: D. 82

    28 times three minus two = 82. The same rule gives every earlier transition.
  6. 6. Continue the descending square numbers: 81, 64, 49, 36, ?
    1. 25
    2. 30
    3. 16
    4. 20

    Reference: q-2b26ed70-58 · Report this question

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    Answer: A. 25

    The terms are 9 squared, 8 squared, 7 squared and 6 squared. Next is 5 squared = 25.
  7. 7. Continue using the sum of the previous two terms: 4, 7, 11, 18, 29, ?
    1. 43
    2. 47
    3. 50
    4. 40

    Reference: q-675ca78a-70 · Report this question

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    Answer: B. 47

    The next term is 18 plus 29 = 47.
  8. 8. Continue by alternating plus five and times two: 3, 8, 16, 21, 42, ?
    1. 84
    2. 45
    3. 47
    4. 49

    Reference: q-920e1cd3-69 · Report this question

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    Answer: C. 47

    After multiplication, the next step adds five: 42 plus five = 47.
  9. 9. Continue by halving each term: 320, 160, 80, 40, ?
    1. 30
    2. 10
    3. 15
    4. 20

    Reference: q-acf87fc0-51 · Report this question

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    Answer: D. 20

    Each term is half the previous one. Half of 40 is 20.
  10. 10. A term starts at 6 and increases by 4 each time. What is the eighth term?
    1. 34
    2. 38
    3. 30
    4. 32

    Reference: q-6e216478-74 · Report this question

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    Answer: A. 34

    The eighth term is seven steps after the first. 6 plus 7 times 4 = 34.

Review your method

Return to the number series and rule selection lesson and identify the reasoning step behind each mistake before repeating the set.

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