# Math Essay

566 WordsApr 22, 20133 Pages
Geometric and Arithmetic Sequences Taurus Corbbrey MAT126 Jerry Bilbrey April1st, 2013 Both Geometric and Arithmetic Sequences are utilized to answer questions 35 and 37 of our text. A geometric sequence is defined as “s a sequence of terms in which each term after the ﬁrst term is obtained by multiplying the preceding term by a nonzero number. This number is called the common ratio.” Further, An Arithmetic Sequence is defined as “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, 2011). By using inductive and deductive reasoning we are able to find the correct mathematical approach to solve these problems. #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 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 the approach I took: We can deduce from the information provided that there is a new price every ten feet as they build the tower. Further, the cost of the labor for each succeeding 10 feet is \$25 more than the preceding 10 feet. With that being said, the next 10 feet will cost \$125, the next 10 feet will cost \$150, etc. What will the total cost of building the tower be? 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 Next, we need to figure out what a9 is.. aN=a1+(n-1)d a9=100+(9-1)25 a9=100+(8)25 a9=100+200 a9=300 Now that we know what a9 is, we need to know what the sum of