Number series and rule selection: guide and free practice

Find an intended number-series rule by testing differences, ratios and alternating positions, then verify that the same rule explains every transition.

Begin with differences

Subtract adjacent terms. Constant first differences suggest addition. A changing difference may itself form a simple sequence. For example, differences of two, four and six suggest that the next difference is eight.

Check multiplication and mixed operations

If terms grow quickly, compare ratios or try multiplication followed by a fixed addition. Explain the operation from every term to the next, rather than fitting only the last two values.

Separate alternating positions

Odd positions and even positions may form independent sequences. Write them on two lines and continue the line containing the missing term. A decreasing sequence interleaved with an increasing one can look irregular until separated.

Use stated constraints

Any finite list can be continued in many mathematically constructed ways. These exercises therefore name the intended rule family, such as repeated differences or alternating operations. The aim is to learn disciplined pattern checking, not to claim that a finite list has only one possible continuation.

Review errors by operation

Keep a short log of whether you missed a difference, ratio, alternating stream or indexing step. The last term given is not necessarily the last term in each sub-sequence. Work without a clock first, then add speed once the operation is reliable.

Your first practice session

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.

Try 10 questions with explanations

Worked examples

  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

    Show answer and solution

    Answer: B. 25

    The next difference is eight. Add eight to 17 to get 25.

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About this practice

These are independently written teaching questions. A practice score helps you review your answers; it is not a validated hiring prediction or an official employer score.