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9th grade · Math · Unit 17 of 18

Sequences

Arithmetic and geometric

What your child practices

Arithmetic and geometric sequences as functions: finding any term, writing a rule, and using a recursive rule.

California Content Standards learning standard: F-IF.3; F-BF.1 · modeling arithmetic patterns and telling them apart from patterns that grow by multiplying

How we explain it

Children can open this short lesson before they practice.

  1. Arithmetic sequences add the same difference d.
  2. Term n = first term + (n − 1) × d.
  3. Geometric sequences multiply by the same ratio.

Example: What is term 10 of 4, 7, 10, 13, ...? d = 3. 4 + 9 × 3 = 31. Answer: 31

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    Which rule gives the sequence 12, 21, 30, 39, ... (n = 1, 2, 3, ...)?

    • a(n) = 12n + 9
    • a(n) = 10n + 2
    • a(n) = 9n + 3
    • a(n) = 9n + 12

  2. Question 2

    a(1) = 3 and a(n) = 3 × a(n − 1). What is a(5)?

    • 243
    • 729
    • 45
    • 15

  3. Question 3

    Is 2, 6, 10, 14, ... arithmetic or geometric?

    • Neither
    • Geometric: multiply by 4
    • Arithmetic: add 4

  4. Question 4

    What is term number 11 of 7, 15, 23, 31, ...?

    answer box

  5. Question 5

    Which rule gives the sequence −3, −1, 1, 3, ... (n = 1, 2, 3, ...)?

    • a(n) = −3n + 2
    • a(n) = 2n − 5
    • a(n) = 2n − 3
    • a(n) = 3n − 6

  6. Question 6

    What is term number 26 of 6, 3, 0, −3, ...?

    answer box

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