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9th grade · Math · Unit 15 of 16

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.

Texas Essential Knowledge and Skills (TEKS) teks student expectation: A.12(C); A.12(D) · arithmetic and geometric sequences

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 Texas

In the Texas Essential Knowledge and Skills (TEKS), this is unit 15 of 16 in 9th grade Math, after Linear or Exponential? and before Rearranging Formulas.

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: Texas Education Agency (TEA)

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 11 of −4, 2, 8, 14, ...?

    answer box

  2. Question 2

    Is 5, 10, 20, 40, ... arithmetic or geometric?

    • Neither
    • Arithmetic: add 5
    • Geometric: multiply by 2

  3. Question 3

    Which rule gives the sequence 0, 4, 8, 12, ... (n = 1, 2, 3, ...)?

    • a(n) = 4n − 4
    • a(n) = 4
    • a(n) = 5n − 5
    • a(n) = 4n

  4. Question 4

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

    • 10
    • 9
    • 16
    • 32

  5. Question 5

    a(1) = 1 and a(n) = 2 × a(n − 1). What is a(4)?

    • 16
    • 8
    • 7
    • 9

  6. Question 6

    Which rule gives the sequence 4, 13, 22, 31, ... (n = 1, 2, 3, ...)?

    • a(n) = 10n − 6
    • a(n) = 9n − 5
    • a(n) = 9n + 4
    • a(n) = 4n + 9

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