Generating Sequences · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Generating sequences from a rule

Mathematics · Algebra · ages 11-14
Name ______________________   Date ____________

  1. A sequence starts at 5. The rule is: add 3 each time. What are the next two terms?

    • 8 and 11
    • 8 and 10
    • 15 and 45
    • 6 and 9

  2. What is the next term? 4, 8, 12, 16, ___

    481216?
    • 18
    • 20
    • 24

  3. In the position-to-term rule 2n + 1, n stands for the position of the term.

    Circle one:   True   False

  4. What is the next term? 20, 17, 14, 11, ___

    20171411?
    • 8
    • 9
    • 7

  5. A sequence uses the position-to-term rule 3n - 2, where n is the position of the term. What is the first term?

    • 1
    • 2
    • 3
    • 5

  6. A sequence starts at 3 and the rule is: multiply by 2 each time. What is the 5th term?

    Answer: ______________

  7. A sequence starts at 100 and the rule is: subtract 7 each time. What is the 4th term?

    Answer: ______________

  8. An arithmetic sequence begins 3, 5, 7 and a geometric sequence begins 2, 6, 18. Add the second term of each sequence together. What do you get?

    Answer: ______________

  9. Priya says 7, 10, 13, 16 is geometric because the numbers keep going up. What's her mistake?

    • The rule multiplies, not adds
    • The numbers should go down, not up
    • The difference is constant, so it's arithmetic, not geometric

  10. In a geometric sequence, the first term is 3 and the third term is 12. What is the second term?

    • 6
    • 8
    • 9
    • 7.5
LightMySky · lightmysky.comW1-mt_yXO7lQ9Yn7-s1

Answer key

For grown-ups. Fold this page away before handing over the rest.

Generating sequences from a rule W1-mt_yXO7lQ9Yn7-s1

  1. 8 and 11 · Adding 3 twice to 5 gives 8, then 11.
  2. 20 · The rule adds 4 each time, so the next term is 16 + 4 = 20.
  3. True · Yes. n is the term's position, so n = 1 gives the first term, n = 2 gives the second, and so on.
  4. 8 · The rule subtracts 3 each time, so the next term is 11 - 3 = 8.
  5. 1 · The first term is at position 1, and 3 x 1 - 2 = 1.
  6. 48 · Doubling step by step gives 3, 6, 12, 24, 48, so the 5th term is 48.
  7. 79 · Counting from 100, the terms are 100, 93, 86, 79, so the 4th term is 79.
  8. 11 · The second terms are 5 and 6, and 5 + 6 = 11.
  9. The difference is constant, so it's arithmetic, not geometric · Each term is 3 more than the last, so it has a constant difference. A constant difference means arithmetic, not geometric.
  10. 6 · Two equal multiplications turn 3 into 12, so each one multiplies by 2. The second term is 3 x 2 = 6.
Worksheet · LightMySky