The world of mathematics is much diversified with the two common and simplest sequences to work with being the arithmetic and geographic sequences. The arithmetic sequence simply entails adding or subtracting the same value to the term therefore coming up with a new one (Russell, 2011, p. 1). This number that is either added or subtracted is referred to as the common difference. A geometric sequence on the other hand involves multiplying or dividing the term with the same value. Subsequently, the number used in the division or multiplication is termed as common ratio. Below are some problems on arithmetic and geometric sequences.
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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 the 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?
This is an arithmetic sequence whereby $25 is being added to every term up to the 90th feet.
- 10th ft. = $ 100
- 20th ft. = $ 125
- 30th ft. = $ 150
- 40th ft. = $175
- 50th ft. = $ 200
- 60th ft. = $ 225
- 70th ft. = $ 250
- 80th ft. = $ 275
- 90th ft. = $ 300
- Total cost = $ 1800
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?
This is a geometric sequence as the money deposited increases at a certain common ratio. The total sum accumulated after the 10 years will thus be calculated as follows (Bluman, 2005, p. 87);
A = P (1 + r)n
- A= This is the total money accumulated after n years.
- P= It is the initial amount of money deposited into the account.
- r= Is the annual interest as a decimal.
- n= Is the number of years the money is invested in the bank.
A = P (1 + r)n
- = 500(1 + (5/100)10
- = 500(1+0.05)10
- = 500(1.05)10
- =500x 1.63
- = $ 814.45
The interest will therefore be the accumulated funds less the initial deposit. That is; ($814.45- $500) = $314.45.
From the above computations, it can be clearly seen that both arithmetic and geometric sequences are applicable in real-life situations. For instance, the first example of the construction industry shows how it is important to have basic knowledge in arithmetic sequences (Russell, 2011, p. 1). This is because without such information, workers will be oppressed in terms of their payment dues. As for the case of the compound interest, it helps the investor to know how much to expect after a certain duration of time (Bluman, 2005, p. 102).
The knowledge of this information is of great essentiality as it is applicable in a number of day to day activities. Some of the common places and situations applicable include in the pension computation, insurance compensation, and financial securities such as share computation just to mention but a few.
Bluman, A. G. (2005). Mathematics in our world (1st ed. Ashford University Custom). United States: McGraw-Hill.
Russell, D. (2011). Arithmetic and Geometric Sequences. Web.