INTRODUCTION

A sequence of number is a list of numbers that are related to each other by a specific rule. Each number in the sequence is called a term of the sequence. The two common types of sequences are the arithmetic sequences and the geometric sequences. Arithmetic sequence is a sequence of numbers in which each succeeding terms differs from the preceding term by the same amount. This amount is known as the common difference (p272). Geometric sequence is 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 (p276).

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?

Here is how it works:

This problem involves arithmetic sequence since the labor cost for each successive ten feet remains constant at $25. The arithmetic sequences of the labor cost are:

10 feet charge = $100

20 feet charge = $125

30 feet charge = $150

40 feet charge = $175

50 feet charge = $200

60 feet charge = $225

70 feet charge = $250

80 feet charge = $275

90 feet charge = $300

To compute the ānā term using the formula from page 273 of Mathematics in Our World, in the pink box. First, is to identify the following given numbers:

n = the number of all terms n = 9

d = the common difference d = 25

a1 = the first term a1 = 100

an = the last term an = a9 (to be computed)

This is the formula to find the nth term of the sequence, or the 9th term in this problem.

an = a1 + (n - 1) d

a9 = 100 + (9 ā 1) 25

a9 = 100 + (8) (25)

a9 = 100 + 200

a9 = 300

The amount of last term is a9 = $300. Now, to find the...