MTH 225: Weekly Challenge 8

--- tags: mth225, weekly-practice --- # MTH 225: Weekly Challenge 8 :::info **Weekly Challenges 8, 9, and 10 are deadline-free.** This means that you may submit your work whenever you believe it is ready to be assessed. However, remember there is one final deadline: *11:59pm Eastern on Sunday, December 12* which is the final deadline for all submissions and revisions of Weekly Challenge work. No submissions or revisions of Weekly Challenges will be accepted past this point. In order to give yourself enough time and space to revise your work on Weekly Challenges 8, 9, and 10, make every effort to submit a completed draft as soon as possible. ::: :::warning **Instructions**: * Your work on Weekly Challenges should consist of **complete solution attempts for all the Application/Extension Problems and complete and thoughtful responses to all the Feedback and Reflection prompts**. Before submitting your work, make sure you've reviewed the [Specifications for Satisfactory Work in MTH 225](/Cy6P0rGZQzuOM3NwZ3ZuMw) document to make sure your work meets the standards to the best of your knowledge. * **Practice Exercises are optional.** You do not need to turn any part of these in. But if you want feedback on any of them, turn those in with the rest of your work and I'll look at it. * You may type up your work or write it by hand on paper, whiteboard, or in a notes app. **Typewritten work is preferred** because it makes revisions easier for you. * If you handwrite your work on paper or a whiteboard, your work needs to be **scanned to a legible, black-and-white PDF**. * All your work is to be submitted as a **single PDF** at the appropriate assignment area on Blackboard in the *Weekly Challenges* folder. Please do not submit multiple PDFs, or files that are not in PDF format. ::: ## Practice Exercises **Practice Exercises are optional and for your benefit only.** You do not need to turn in work or answers unless you want feedback on your work. *Sequences:* Classify each of these sequences as arithmetic, geometric or neither. For the ones that are arithmetic or geometric, state the common amount or common ratio between terms, and find both a closed formula and a recursive definition for the sequence. * 3, 8, 13, 18, 23, 28, ... * 100, 10, 1, 0.1, 0.01, ... * 1, 2, 3, 2, 3, 4, 3, 4, 5, 4, 5, 6, ... * 2, .2, .02, .002, .0002, ... ## Application/Extension Problems Choose **any two (2) of the following four problems** to work. *Do not submit work on more than two of these.* 1. Work Exercise #12 in [Section 2.2](http://discrete.openmathbooks.org/dmoi3/sec_seq-arithgeom.html) of your textbook. 2. Work Exercise #13 in [Section 2.2](http://discrete.openmathbooks.org/dmoi3/sec_seq-arithgeom.html) of your textbook. 1. Work Exercise #14 in [Section 2.2](http://discrete.openmathbooks.org/dmoi3/sec_seq-arithgeom.html) of your textbook. 4. Write a Python function called `sequence_info` that does the following: - The function takes a list as input, that contains at least the first five elements of a sequence. Giving it more than five terms is OK. - The function determines if the sequence --- as given by the list that the user inputs --- is arithmetic, geometric, or neither. - If the sequence is *arithmetic*, the function prints a message to the screen stating so, and also stating what the common amount between terms is. - If the sequence is *geometric*, the function prints a message to the screen stating so, and also stating what the common ratio between terms is. - If the sequence is *neither arithmetic nor geometric*, the function prints a message to the screen saying so. Here are some sample inputs and outputs, to show what calling the function should look like and to give you sample results to check your work against. ``` > sequence_info([1,2,3,4,5,6]) > The sequence is arithmetic with common amount 1. > sequence_info([2,4,8,16,32]) > The sequence is geometric with common ratio 2. > sequence_info([1,1,2,3,5,8,13]) > The sequence is neither arithmetic nor geometric. ``` Some assumptions and requirements for this: - You may assume that the user never gives an input list shorter than 5 elements, and never gives input that is not a list. - Your function must be called `sequence_info`. You may not rename it. (Your code will be graded by running it on a large number of test cases, and this won't work unless the name is `sequence_info`.) - Your code must use the `print` command, not `return`, to print the information to the screen. - Only functions from the standard library are allowed. You may not use functions from any other modules or libraries. ## Feedback and Reflection