---
tags: mth225, dailyprep
---

# Daily Prep 5.1 -- MTH 225

## Overview

Our final module in the course is all about *recursion*. We begin this module with a basic tool for thinking about recursion, the **integer sequence**. We'll look at sequences of integers arising from different places (visual patterns, formulas, etc.) and think about how to write them **recursively** and using **closed formulas**.

## Learning objectives

**Basic Learning Objectives:** *Before* our class meeting, use the Resources listed below to learn all of the following. You should be reasonably fluent with all of these tasks prior to our meeting; we will field questions on these, but they will not be retaught.

* Identify the terms and indices in a sequence.
* Compute values in a sequence defined as a closed formula.
* Compute values in a sequence defined as a recurrence relation.

**Advanced Learning Objectives:** *During and after* our class meeting, we will work on learning the following. Fluency with these is not required prior to class.

* Given a sequence arising from a visual pattern or just given as a list of terms, write a recursive definition or closed formula for it.

## Resources for learning

**Video:** Watch this from [the MTH 225 playlist](https://vimeo.com/showcase/8667148) (total running time 11:02):

<iframe src="https://player.vimeo.com/video/635492325" width="640" height="564" frameborder="0" allow="autoplay; fullscreen" allowfullscreen></iframe>

**Text:** This material is discussed in [Section 2.1 of your textbook](http://discrete.openmathbooks.org/dmoi3/sec_seq_intro.html).

You are free to search for and use other resources in addition to, or instead of the above, as long as you can work the exercises below.

## Exercises

Once you have watched the videos above, go to this form and complete all the non-optional items on it:

https://docs.google.com/forms/d/e/1FAIpQLSdjpPJMTYZctW1RwO25yn7v6TJIMsRtbeIc85R38BlMf8A7Vw/viewform

## Submission and grading

**Submitting your work:** Your work is submitted when you submit the Google Form. You should receive an email receipt indicating that the work was submitted successfully.

**How this is graded:** The pre-class portion of the Daily Prep is graded either 0 points or 1 point, on the basis of completeness and effort. Wrong answers are not penalized. Earning a "1" requires that you:

- Turn the work in before its deadline;
- Leave no item blank or skipped, even accidentally; and
- Give a good-faith effort at a correct answer on every non-optional item.

More information can be found in the [Specifications for Satisfactory Work in MTH 225](/Cy6P0rGZQzuOM3NwZ3ZuMw) document.

When you arrive for the class meeting, you'll be put into a group of 2-3 to complete a quiz over this material, which will be graded on a 0/1 scale on the basis of correctness.