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9th grade · Math · Unit 17 of 17

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.

Arizona Academic Standards learning standard: A1.F-IF.A.3; A1.F-BF.A.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

Sequences in Arizona

In the Arizona Academic Standards, this is unit 17 of 17 in 9th grade Math, after Two-Way Tables & Causation.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Arizona Department of Education

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 6, 14, 22, 30, ... (n = 1, 2, 3, ...)?

    • a(n) = 8n − 2
    • a(n) = 8n + 6
    • a(n) = 9n − 3
    • a(n) = 6n + 8

  2. Question 2

    Is 5, 15, 45, 135, ... arithmetic or geometric?

    • Geometric: multiply by 3
    • Arithmetic: add 10
    • Neither

  3. Question 3

    a(1) = 5 and a(n) = 2 × a(n − 1). What is a(3)?

    • 20
    • 9
    • 40
    • 30

  4. Question 4

    What is term number 29 of −4, −9, −14, −19, ...?

    answer box

  5. Question 5

    a(1) = 4 and a(n) = 3 × a(n − 1). What is a(3)?

    • 34
    • 10
    • 108
    • 36

  6. Question 6

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

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

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