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Week 1 Assignment
MAT 126: Survey of Mathematical Methods
35: 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 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?
Here is how I think about it: I see that there is a new price every 10 feet. Each new price is $25 added to the previous price. The repeated addition tells us this is an arithmetic sequence. First, I will need to identify the following numbers.
n=the number of terms altogether n=9
d= the common difference d=25
a1= the first term a1=100
an= the last term an=a9 (yet to be computed)
Next I need to compute what a9 is. This is the formula to find the nth term of the sequence, or the 9th term in this case.
an=a1 + (n – 1)*d
a9=100 + (9 -1) *25
a9=100 + 8 *(25)
a9=100 + 200
Now that I know what a9 is, I need to know what the sum of the sequence is for a1 to a9
Sn = (1/2) * n (a1 + an)
S9= (1/2) *9 (100 + 300)
S9= (1/2) *9* (400)
The final answer is: $1,800
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?
Here is how I think about it: Each year 5% interest is added to the balance. I will use B as my balance.
B + Balance
B + (0.5) b
Each year the existing balance is multiplied by 1.05. This is repeated by the same numbers it tells us that we have a geometric sequence. First I need to identify the following numbers.
n= the number of terms n=10
r= the common ratio r=1.05
a1= first term a1=525
500(1.05) = 525 for the balance at the end of the first...
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