Real world applications
XXX
MAT126: Survey of Mathematical Methods
Instructor: XXX
May 20, 2012
In this assignment I would like to talk about arithmetic sequences and geometric sequences and want to give an example each how to calculate with those sequences. First I want to give a short definition of each sequence.
“An arithmetic sequence is a sequence of numbers in which each succeeding term differs from the preceding term by the same amount. This amount is known as the common difference.” (Bluman, A. G. 2500, page 221)
An example for an arithmetic sequence is:
1, 3, 5, 7, 9, 11, … (The common difference is 2. (Bluman, A. G. 2500, page 221)
“A geometric sequence is a sequence of terms in which each term…show more content… Now we use the following formula to find out how much we have after 10 years: an = a1 (r n-1) a10 = 525(1.059) a10 = 525(1.551328216…) a10 = 814.4473131 a10 = $ 814.85
Thus, the balance in the savings account at the end of 10 years will be $ 814.85.
Here we have a geometric sequence. This repeated multiplication by the same number tells us we have a geometric sequence. In this case we add every year 5% the $ 500. The difference to an arithmetic sequence is that the 5% are added every year to the $ 500 including the 5%. We are starting with $ 500 only in year one. The first year we have $ 500 and add 5%. So we have in the second year 525 $. We add now the 5% to the $ 525. In the third year we add the 5% to that what we have at the end of the second year and so on.
I have selected the formulas to solve the exercises after I have thought about what exercise what sequence is. Since in the exercise with the CB radio tower the costs were always $ 25 more for every 10 feet I used the formula for arithmetic sequences. It was always x + $ 25. So it is an arithmetic sequence. The other exercise includes a geometric sequence since always 5% annual interest is added that is compounding yearly. Already in the second year we start no more with $ 500. Therefor it is a geometric sequence.
In this week I have learned what sequences are and the difference between arithmetic
