# Real World Applications Essay

680 Words3 Pages
Week 1 Assignment – Real World Applications MAT 126 January XX, 20XX Real World Applications In lieu of not having a book on time to complete this assignment, I took the proactive approach to researching and solving the questions we needed to respond to. Upon my findings, because the question had recurrent additions, that tells us that in order to solve the question, we must apply an arithmetic sequence. There is a value in understanding how to comprehend and apply arithmetic sequence (otherwise known as arithmetic progression) in the real world, especially when trying to apply it to things such as Microsoft Excel. I’ve provided an example of doing it in Excel in the “long” fashion along with doing it by the equation. The Problem A person hired a firm to build a CB radio tower. The firm charges \$100 for labor for the first 10 feet. After that, the cost of the labor for each succeeding 10 feet is \$25 more than the preceding 10 feet. That is, the next 10 feet will cost \$125, the next 10 feet will cost \$150, etc. How much will it cost to build a 90-foot tower? The Thought Process The upfront cost the firm charges for the first 10 feet is \$100. For each succeeding 10 feet, the cost is \$25 more than the preceding 10 feet. The total number of times (or terms as used in the example) is n=9 (90/10=9). The common cost difference is d=\$25. In this case, the first “term”, which means the first 10 feet costs a1=\$100. The last term is what we are trying to get. That is an=a9. Our goal is to find out what “n” equals here. By using the formula provided within the text and found online when researching arithmetic sequence, we can find out the nth term of the sequence. an=a1+(n-1)d a9=100+(9-1)(25) a9=100+(8)(25) a9=100+200 a9=300 Now we need to figure out the sum of the sequence from a1 to a9. Below is the work to get the solution. Sn=n(a1+a9)