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Mathematics of Sequences and Financial Growth: Arithmetic and Geometric Applications

An assignment exploring arithmetic and geometric sequences and their financial growth applications.

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    Mathematics of Sequences and Financial Growth: Arithmetic and Geometric Applications Mathematics - Problems #35 & 37 #35. A person hired a firm to build a CB radio tower. The firm charges $100 for labor for first 10 feet. After that, the cost of 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? Does this problem involve Arithmetic sequence or a Geometric sequence? And use the proper formulas where applicable. This is an arithmetic Sequence. First we have to figure out identities of all of our numbers. The letter n will stand for the number of terms, d will stand for the common differenc e, a 1 is the first term and an as the last term. In other terms n=9, d=25, a=100, and an=a 15 . The problem to figure out is what a9 is. Using the formula an=a1 + (n - 1)d I fill in all of my numbers and then have a 9 =100 +(9 - 1)(25). First I subtract the (9 - 1) which comes to 8. Now my problem looks like a 9 =100 + (8)25. After subtracting that, I need to multiply 8 times 25. My answer comes to 200. Now I have a 9 =100 + 200. Narrowing the problem I add the 200 and 100 together and I come up with 300. So now I know that a 9 equals 300. My next step is to figure out what a 9 is. Using the formula sn=n(a1 + a9) divided by 2. So after adding all of my numbers in, I have sn=9(100 + 300) divided by 2. When after doing the entire math, my problem should be Sn = 9 times 400 and divided that by 2. My last step is to divide 9 by 2 which are 4. 5 and then multiply 4 .5 times 400 which my total will then come to 18 00. So my total for 90 feet will be $ 18 00. 37. A person deposited $500 in a savings account that pays 5% annual interest that is compounded yearly, at the end of 10 years, how much money will be in the savings account? Does this problem involve Arithmetic sequence or a Geometric sequence? And use the proper formulas where applicable.

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