The goal of this lesson is for students to understand that how an equation is written to represent a function depends on how the domain of a function is identified. With sequences, it is common to start at either or . So far in this unit, the first term has been cited as . The exception has been when is confusing given the context, which is the case when the number of pieces of paper depends on the number of cuts. This lesson returns to the paper cutting context and gives students a chance to study the effect this choice has when writing an equation to define a sequence. This lesson is also meant to help students review how to write equations of linear and exponential functions by using a table to express regularity in repeated reasoning (MP8). In the following lessons, students will write equations for these types of functions in various contexts.

Prior to this lesson students focused on using function notation to define sequences recursively. In this lesson, students will study equations representing functions that are known as explicit or closed-form definitions. A closed-form definition is one where the value of the term is determined only from the term number. This type of equation is one students are familiar with from their earlier work with linear and exponential equations.

A focus of this lesson is using precise language (MP6) to explain patterns and understand how a function can be represented by two different equations.

Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.