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Number sequences

Find the next number in an increasing or decreasing sequence.

Practice + answer key · 2 pages

Worksheet settings12 questions · 2 columns · A4
Starting values

The first term is in this range. Later terms follow a fixed nonzero difference.

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Number sequencesNumber sequences. Practice. Write the next term: −3, −2, −1, 0, __. Write the next term: 18, 9, 0, −9, __. Write the next term: 20, 24, 28, 32, __. Write the next term: −9, −11, −13, −15, __. Write the next term: 16, 11, 6, 1, __. Write the next term: 0, 4, 8, 12, __. Write the next term: −7, −15, −23, −31, __. Write the next term: 11, 6, 1, −4, __. Write the next term: −9, −10, −11, −12, __. Write the next term: 15, 12, 9, 6, __. Write the next term: −7, −3, 1, 5, __. Write the next term: 17, 15, 13, 11, __.Name __________________________Date _______________Number sequencesWrite the next number in each sequence.Worked exampleFind the next term: 12, 9, 6, 3, __. → 09 − 12 = −3.1.Write the next term: −3, −2, −1,0, __.2.Write the next term: 18, 9, 0,−9, __.3.Write the next term: 20, 24, 28,32, __.4.Write the next term: −9, −11,−13, −15, __.5.Write the next term: 16, 11, 6,1, __.6.Write the next term: 0, 4, 8, 12,__.7.Write the next term: −7, −15,−23, −31, __.8.Write the next term: 11, 6, 1,−4, __.9.Write the next term: −9, −10,−11, −12, __.10.Write the next term: 15, 12, 9,6, __.11.Write the next term: −7, −3, 1,5, __.12.Write the next term: 17, 15, 13,11, __.MathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 1mathsprig-1 · mathsprig-v1 · 91b13bb0
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Practice + answer key · 2 pages

Algebra

What you’ll practice

Find the next term of an arithmetic sequence.

Look for the same difference between each pair of neighboring terms. Check it in more than one place, then use it to find the next number.

How this skill works

Subtract the first term from the second to find a possible difference.

Check that difference against the next pairs, then add it to the final visible term.

Worked example

Find the next term: 12, 9, 6, 3, __.
  1. 9 − 12 = −3.
  2. Every step subtracts 3.
  3. 3 − 3 = 0.

Answer: 0

Teaching notes

  • Check more than one step before deciding on a rule.
Practice questions
  1. Write the next term: −3, −2, −1, 0, __.
  2. Write the next term: 18, 9, 0, −9, __.
  3. Write the next term: 20, 24, 28, 32, __.
  4. Write the next term: −9, −11, −13, −15, __.
  5. Write the next term: 16, 11, 6, 1, __.
  6. Write the next term: 0, 4, 8, 12, __.
  7. Write the next term: −7, −15, −23, −31, __.
  8. Write the next term: 11, 6, 1, −4, __.
  9. Write the next term: −9, −10, −11, −12, __.
  10. Write the next term: 15, 12, 9, 6, __.
  11. Write the next term: −7, −3, 1, 5, __.
  12. Write the next term: 17, 15, 13, 11, __.
Answers and steps
  1. 1
    1. Each step adds 1.
    2. 0 + (1) = 1.
  2. −18
    1. Each step adds −9.
    2. −9 + (−9) = −18.
  3. 36
    1. Each step adds 4.
    2. 32 + (4) = 36.
  4. −17
    1. Each step adds −2.
    2. −15 + (−2) = −17.
  5. −4
    1. Each step adds −5.
    2. 1 + (−5) = −4.
  6. 16
    1. Each step adds 4.
    2. 12 + (4) = 16.
  7. −39
    1. Each step adds −8.
    2. −31 + (−8) = −39.
  8. −9
    1. Each step adds −5.
    2. −4 + (−5) = −9.
  9. −13
    1. Each step adds −1.
    2. −12 + (−1) = −13.
  10. 3
    1. Each step adds −3.
    2. 6 + (−3) = 3.
  11. 9
    1. Each step adds 4.
    2. 5 + (4) = 9.
  12. 9
    1. Each step adds −2.
    2. 11 + (−2) = 9.