Geometric and Arithmetic Sequences to Questions 35 & 37
MAT-126: Survey of Mathematical Methods(ACO1141A)
October 11, 2011
As one observes an arithmetic sequence, it is imperative to use inductive and deductive reasoning to use the right mathematical approach of geometric or arithmetic sequence to solve the equation in the most pragmatic way. Most times both inductive and deductive reasoning is used on an equation or variable to come up with the most direct approach to an answer (Bluman, 2005).
The first problem # 35 asks: “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?” I used deductive reasoning and the arithmetic approach to come up with my solution to this equation. I drew a graph:
Simple addition of: 100+125+150+175+200+225+250+300+325=$1800. The cost will be $1800. A=100, d=25, n=9.
The second question # 37 asks: “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?” For this answer I used the geometric sequence: P is the $500 deposited. R is the 5% annual interest. N is the 10 years. A is the amount of money that has been accumulating over the past N years. A=P (1+R) N. The amount accrued would be $814.45, hence, 500(1+0.05)10=814.45 (Bluman, 2005).
In conclusion, I find deductive and inductive reasoning used at the same time in one mathematical equation, strongly enhances ones ability to come up with a correct solution to a problem (Bluman, 2005)....
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