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 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 difference, a1 is the first term and an as
the 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 I
subtract the (9-1) which comes to 8. Now my problem looks like a9=100 + (8)25. After subtracting that, I
need to multiply 8 times 25. My answer comes to 200. Now I have a9=100 + 200. Narrowing the problem
I add the 200 and 100 together and I come up with 300. So now I know that a9 equals 300.
My next step is to figure out what a9 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 1800. So my total for 90 feet will be
$1800.
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.
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 difference, a1 is the first term and an as
the 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 I
subtract the (9-1) which comes to 8. Now my problem looks like a9=100 + (8)25. After subtracting that, I
need to multiply 8 times 25. My answer comes to 200. Now I have a9=100 + 200. Narrowing the problem
I add the 200 and 100 together and I come up with 300. So now I know that a9 equals 300.
My next step is to figure out what a9 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 1800. So my total for 90 feet will be
$1800.
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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Subject
Mathematics