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9th grade · Math · Unit 17 of 22

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.

New York State Learning Standards learning standard: AI-F.IF.3; AI-F.BF.1 · sequences as functions, and telling patterns that add from patterns that multiply

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 New York

In the New York State Learning Standards, this is unit 17 of 22 in 9th grade Math, after Two-Way Tables & Causation and before Graphs of Equations & Inequalities.

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: New York State Education Department (NYSED)

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

    What is term number 27 of −2, −8, −14, −20, ...?

    answer box

  2. Question 2

    Is 4, 8, 16, 32, ... arithmetic or geometric?

    • Geometric: multiply by 2
    • Arithmetic: add 4
    • Neither

  3. Question 3

    Which rule gives the sequence 8, 11, 14, 17, ... (n = 1, 2, 3, ...)?

    • a(n) = 8n + 3
    • a(n) = 3n + 8
    • a(n) = 4n + 4
    • a(n) = 3n + 5

  4. Question 4

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

    • 12
    • 24
    • 7
    • 18

  5. Question 5

    What is term number 22 of 0, 8, 16, 24, ...?

    answer box

  6. Question 6

    Which rule gives the sequence 5, 7, 9, 11, ... (n = 1, 2, 3, ...)?

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

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