Math 1 · Unit 9 · Lesson 1

A Sequence Is a Function

A sequence is a list of numbers in order. Each number is a term, and each term has a position, its term number. Position in, term out: that is a function from Unit 2, with only whole numbers allowed as inputs, so its graph is separate dots. A list that adds the same amount each time is arithmetic, the line family as a list. A list that multiplies by the same number is geometric, the exponential family as a list.

About 40 minutes Position in, term out

The big idea

A sequence is a list of numbers in a set order, and it is a function. The term number is the input and the term is the output, and each position holds exactly one term, so it passes the function test from Unit 2. The inputs are only whole numbers, 1, 2, 3, and so on, because there is no position 2.5, so a sequence is discrete and its graph is separate dots, never a solid line or curve. The notation a sub n names the term in position n, and f(n) says the same thing in function notation. Adding gives arithmetic, multiplying gives geometric: an arithmetic sequence is the line family in list form, and a geometric sequence is the exponential family in list form. Some sequences, like the square numbers and the Fibonacci numbers, are neither.

The parts of this lesson

Each part is its own short page. Go in order, or pick the one you need.

1The Words We UseThe vocabulary for this lesson, in one place.Start here 2Two families, now as listsThis unit has almost no new math in it. 3A sequence is a function made of dotsA sequence is a list of numbers in a set order. 4Some lists are neitherNot every list adds or multiplies. 5Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with sequence, term, and term number, why a sequence is a function, domain and range, dots not lines, the two notations, and the adds-multiplies-or-neither check. Plus a worksheet with an answer key and a short lesson plan.

Study guide (PDF) Worksheet and answer key (PDF) Lesson plan (PDF)

Where this goes next

Previous lesson: When Money Shrinks, and Using the ModelsThe end of Unit 8. Next lesson: Arithmetic Sequences, Lines Made of DotsLists that add: the common difference is the slope. Back to the Math 1 mapEvery Math 1 lesson, in course order. Tell us what you thoughtA few quick questions about this lesson. It takes a minute, and it is how the lesson gets better.

NC Math 1 standards in this lesson: NC.M1.F-IF.3 (sequences are functions whose domain is a subset of the integers), NC.M1.F-IF.2 (function notation in context), NC.M1.F-IF.5 (domain and range in context).