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

Finding the nth-term rule

Mathematics · Algebra · ages 12-14
Name ______________________   Date ____________

  1. What is the common difference of the sequence 5, 9, 13, 17?

    591317
    • 3
    • 4
    • 5

  2. The rule is 4n - 1. What is the 50th term?

    • 200
    • 199
    • 196
    • 149

  3. The sequence 5, 9, 13, 17, ... follows the rule 4n + 1. What is the 6th term?

    Answer: ______________

  4. The number multiplied by n in an nth-term rule is always the sequence's common difference.

    Circle one:   True   False

  5. What is the nth-term rule for 2, 5, 8, 11, ...?

    • 3n + 2
    • 2n + 3
    • 3n - 1
    • n + 3

  6. Is 47 a term in the sequence with rule 6n + 5?

    • Yes, it's the 7th term
    • No, n works out to a fraction
    • Yes, it's the 8th term

  7. What is the 100th term of the sequence with rule 3n + 2?

    Answer: ______________

  8. A sequence has the rule 3n + 4. What is its zero term?

    • 0
    • 3
    • 4

  9. The sequence 8, 5, 2, -1 goes down by 3 each time. Jamal says its rule is 3n + 11. Testing n = 1 gives 3 x 1 + 11 = 14, but the first term is 8. Is Jamal's rule right?

    • No, the common difference is negative, so it should be -3n + 11
    • Yes, that's correct
    • No, the zero term should be 3 instead of 11

  10. The sequence 10, 17, 24, 31, ... has the rule 7n + 3. What is the 12th term?

    Answer: ______________

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Answer key

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

Finding the nth-term rule W1-mt_HRKzwEQJgO-s1

  1. 4 · Each term is 4 more than the last: 9 - 5 = 4, 13 - 9 = 4.
  2. 199 · Substitute n = 50: 4 x 50 - 1 = 199.
  3. 25 · Substitute n = 6: 4 x 6 + 1 = 25.
  4. True · That number tells you how much the sequence changes each step, which is exactly the common difference.
  5. 3n - 1 · The gap is 3 and the term before the first is -1, so the rule is 3n - 1.
  6. Yes, it's the 7th term · Set 6n + 5 = 47, so 6n = 42 and n = 7. Since 7 is a whole number, 47 is the 7th term.
  7. 302 · Substitute n = 100: 3 x 100 + 2 = 302.
  8. 4 · Plug n = 0 into the rule: 3 x 0 + 4 = 4. That's the zero term, not the answer 0.
  9. No, the common difference is negative, so it should be -3n + 11 · The sequence decreases by 3 each step, so the common difference is -3, not 3. The correct rule is -3n + 11, which gives 8 when n = 1.
  10. 87 · Substitute n = 12: 7 x 12 + 3 = 87.
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