Arithmetic and Geometric Sequences

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Arithmetic and Geometric Sequences A sequence is a set of numbers, which are called terms and are in some particular order; as explained in our text, “ This set or list of numbers are related to each other by a specific rule” (Bluman, 2011). In this paper two real world applications, one arithmetic and one geometric sequence will be resolve. The purpose of this is to compare the difference between both of them and to show what procedures are needed to resolve the problems in order to obtain an answer. It is said that the arithmetic sequence is a set 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). The following exercise will show us how to find the nth term of an arithmetic sequence and to find the sum of the terms. a) 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? As we can see in the exercise the firm charges $100 for building the first 10 feet of the tower and adds a $25 fee for every 10 feet to the previous price. The repeated addition proves us that this is an arithmetic sequence. In order to resolve this we 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) We need to find what a9 is; therefore, we need to use the formula located in page 271 of Mathematics in Our World. This formula will help us find the nth term of the sequence and in this case it will be the 9th term. an = a1 + (n – 1)d a9 =

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