---
tags: mth225, dailyprep
---

# Daily Prep 5.4 -- MTH 225

## Overview

This lesson is essentially a practice session, with no new material --- but focusing on one task, namely **finding recurrence relations for recursively-defined sequences**. We've seen that this is fairly easy for arithmetic and geometric sequences. But what happens when you have a more complicated sequence? We'll play around with several and try to get the hang of this process.

## 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.

- *(Review)* Find a recursive definition (initial condition plus recurrence relation) for an arithmetic sequence.
- *(Review)* Find a recursive definition (initial condition plus recurrence relation) for a geometric sequence.

**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.

- Find a recursive definition for a sequence that is neither arithmetic nor geometric.

## Resources for learning

There's no video or text to review this time, but you might benefit from reviewing the previous Module 5 material on recurrence relations.

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

All the exercises are found in this Google Form:

https://docs.google.com/forms/d/e/1FAIpQLSfs88FP0Zwwqo2GSEWz-KcmqPHVNTOBuZQ9AkU4WfQJ8tkClw/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.