CurriculumGrade 9Mathematics

Sequences as Functions

Aligned to F-IF.A.3 — Common Core State Standards for Mathematics.

What this lesson teaches

A sequence is a function whose inputs are whole-number positions (1, 2, 3, …) and whose outputs are the terms. It can be given by a formula or defined recursively from the previous term.

Worked example

A sequence starts at 5 and adds 3 each time: a(1) = 5 and a(n) = a(n−1) + 3. Then a(2) = 8, a(3) = 11, and a(4) = 14.

Practice questions

  1. List the first four terms of a(n) = 2n + 1.
  2. A sequence has a(1) = 10 and a(n) = a(n−1) − 4. Find a(2) and a(3).
  3. Write a recursive rule for the sequence 3, 6, 9, 12, ….

Watch the lesson

Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.

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En español

Sucesiones como Funciones

Una sucesión es una función cuyas entradas son posiciones enteras (1, 2, 3, …) y cuyas salidas son los términos. Se puede dar con una fórmula o definir de forma recursiva a partir del término anterior.

Ejemplo: Una sucesión empieza en 5 y suma 3 cada vez: a(1) = 5 y a(n) = a(n−1) + 3. Entonces a(2) = 8, a(3) = 11 y a(4) = 14.

More Functions lessons

Interpreting Graphs of FunctionsF-IF.B.4What Is a Function?F-IF.A.1Evaluating FunctionsF-IF.A.2Domain in ContextF-IF.B.5Average Rate of ChangeF-IF.B.6Graphing Key FeaturesF-IF.C.7

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