Sequences Defined by an Explicit Formula

If you plan to learn calculus, this introduction to sequences and series will be very helpful. The first topic you will explore is how to write the terms of a sequence given a formula.

Sequences and Their Notations

Learning Objectives

In this section, you will:

  • Write the terms of a sequence defined by an explicit formula.
  • Write the terms of a sequence defined by a recursive formula.
  • Use factorial notation.

A video game company launches an exciting new advertising campaign. They predict the number of online visits to their website, or hits, will double each day. The model they are using shows 2 hits the first day, 4 hits the second day, 8 hits the third day, and so on. See Table 1.

Day 1 2 3 4 5 …
Hits 2 4 8 16 32 …

Table 1

If their model continues, how many hits will there be at the end of the month? To answer this question, we'll first need to know how to determine a list of numbers written in a specific order. In this section, we will explore these kinds of ordered lists.

Source: Rice University, https://openstax.org/books/college-algebra/pages/9-1-sequences-and-their-notations
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