---
# System prepended metadata

title: Daily Prep 5.3 -- MTH 225
tags: [' dailyprep', mth225]

---

---
tags: mth225, dailyprep
---

# Daily Prep 5.3 -- MTH 225

## Overview

In this lesson we focus on two specific kinds of sequences, which you've encountered in the previous two lessons: **arithmetic** sequences (where the terms change by a constant amount) and **geometric** sequences (where the terms change by a constant multiple or factor). These turn out to be quite simple to describe with a closed formula or a recursive definition, and we'll use that fact to build some formulas for the partial sums of these sequences. 

## 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 a sequence as arithmetic, geometric, or neither. 
- If a sequence is arithmetic, determine the constant amount by which the terms change. 
- If a sequence is geometric, determine the constant multiply by which the terms change. 
- Find the $n$th term of an arithmetic or 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. 

- Given an arithmetic sequence, express it in closed form and using recursion.
- Given a geometric sequence, express it in closed form and using recursion.
- Find a formula for the $n$th partial sum of an arithmetic sequence. 
- Find a formula for the $n$th partial sum of a geometric sequence. 



## Resources for learning

**Video:** Watch this from [the MTH 225 playlist](https://vimeo.com/showcase/8667148) (total running time 7:25): 

<div style="padding:56.25% 0 0 0;position:relative;"><iframe src="https://player.vimeo.com/video/638676941?h=571cb25e8a&amp;badge=0&amp;autopause=0&amp;player_id=0&amp;app_id=58479" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen style="position:absolute;top:0;left:0;width:100%;height:100%;" title="Screencast 5.3: Arithmetic and geometric sequences"></iframe></div><script src="https://player.vimeo.com/api/player.js"></script>


**Text:** This material is discussed in [Section 2.2 of your textbook](http://discrete.openmathbooks.org/dmoi3/sec_seq-arithgeom.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/1FAIpQLSeIfcvVjbcveWo4HpiQVYpEY9X41UeYTrcGKUgX0b74l7ngtg/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. 