Subscribe

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.

Maine Learning Results learning standard: HSF.IF.A.3; HSF.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 Maine

In the Maine Learning Results, 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: Maine 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

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

    • 27
    • 81
    • 9
    • 25

  2. Question 2

    Which rule gives the sequence 7, 11, 15, 19, ... (n = 1, 2, 3, ...)?

    • a(n) = 7n + 4
    • a(n) = 5n + 2
    • a(n) = 4n + 3
    • a(n) = 4n + 7

  3. Question 3

    What is term number 14 of −5, −6, −7, −8, ...?

    answer box

  4. Question 4

    Is 4, 12, 36, 108, ... arithmetic or geometric?

    • Geometric: multiply by 3
    • Neither
    • Arithmetic: add 8

  5. Question 5

    a(1) = 4 and a(n) = 2 × a(n − 1). What is a(3)?

    • 16
    • 24
    • 8
    • 32

  6. Question 6

    Is 1, 4, 7, 10, ... arithmetic or geometric?

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

More 9th grade