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 examples
Example 1
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.
Example 2
The same sequence explicitly: a(n) = 5 + 3(n − 1) = 3n + 2. Explicit gives any term directly; recursive needs the one before.
Example 3
A sequence's domain is the counting numbers, which is why its graph is dots and not a line.
Practice questions
- List the first four terms of a(n) = 2n + 1.
- A sequence has a(1) = 10 and a(n) = a(n−1) − 4. Find a(2) and a(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.
▶ Watch this lessonEn 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 1: 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.
Ejemplo 2: La misma sucesión de forma explícita: a(n) = 5 + 3(n − 1) = 3n + 2. La explícita da cualquier término directo; la recursiva necesita el anterior.
Ejemplo 3: El dominio de una sucesión son los números naturales, por eso su gráfica son puntos y no una recta.
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