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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.

Ethan Wilson
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Mathematics of Sequences and Financial Growth: Arithmetic and Geometric ApplicationsMathematics-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 oflabor 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?Anduse the properformulas where applicable.This is anarithmeticSequence. First we have to figureout identitiesof all ofournumbers. The letter nwill stand for the number of terms, d will stand for thecommondifference, a1is the first term andan asthe last term. In other terms n=9, d=25, a=100, and an=a15. 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 a9=100 +(9-1)(25). First Isubtract the (9-1) which comes to 8. Now my problem looks like a9=100 + (8)25. After subtracting that, Ineed to multiply 8 times 25. My answer comes to 200. Now I have a9=100 + 200. Narrowing the problemI add the 200 and 100 together and I come up with 300. So now I know that a9equals 300.My next step is to figure out whata9is. Using the formula sn=n(a1 +a9) divided by 2. So afteradding all of my numbers in, I have sn=9(100 + 300) divided by 2. When after doingthe entiremath, myproblem should beSn= 9 times 400 and divided that by 2. My last step is to divide 9by 2 whichare4.5and then multiply 4.5 times 400 which my total will then come to1800. So my total for 90 feet will be$1800.37.A person deposited $500 in a savings account that pays 5% annual interest that iscompounded yearly,atthe end of 10 years, how much money will be in the savings account?Does this problem involve Arithmetic sequence or a Geometric sequence?Anduse the properformulas where applicable.

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