Arithmetic Sequence is 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 and can be found using a specific formula by substituting the numbers from the word problem into the equation. When you plug in all the information, you are able to find out the money that needs to be spent and saved in the following word 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 $125 more than the preceding 10 feet will cost $125, the next ten feet will cost $150 etc. How much will it cost to build a 90 foot tower?
an=a1+ (n1) d
a125=100+ (1251) (150)
a125=100+124(150)
a125=100+18600
a125=18700
sn =n (a1 + an) / 2
= 125 (100+18700) /2
=125(1880) /2
=62.5 (18800) =1175000
The cost to build a 90foot tower is $11,750.
37. A person deposited $500 in a savings account that pays 5% annual interest that is compound yearly. At the end of 10 years, how much money will be in the savings account?
S+ (0.5) S n=10
S+ (1+0.5) r=1.05
S (1.05) a1= 500(1.05) =525
an= a1(rn1)
a10=525(1.059)
a10=525(1.551328216)
a10=814.4473134
The balance in the savings account at the end of 10 years will be $814.44.
I chose to use the Arithmetic and geometric sequence because the formula made the answer easier to find the first term and the common difference. All you needed to do was find the formula and plug the numbers from the word problem to get the answer. I could apply this knowledge to real world situations because you can use this when you are checking to see how much money will be in your savings account and how much money...
...Anatolia College 
Mathematics HL investigation

The Fibonacci sequence 
Christos Vassos

Introduction
In this investigation we are going to examine the Fibonacci sequence and investigate some of its aspects by forming conjectures and trying to prove them. Finally, we are going to reach a conclusion about the conjectures we have previously established.
Segment 1: The Fibonacci sequence
The Fibonacci sequence...
...the graph that the pattern/structure is exponential. This is due to the previous numbers being added in succession with the next, resulting in the ‘gap’ between each number to increase.
The trend in which the numbers follow is called a Fibonacci sequence and is often found in nature as well.
Many instances in which the Fibonacci Series is present in nature are that a lot of flowers and cone shaped structures have the number of petals as one of the Fibonacci numbers....
...Higher Arithmetic
Higher arithmetic, also known as the theory of numbers, is known for its basics of the natural numbers, simple numbers. The numbers, 1, 2, and 3 are numbers that are known as natural numbers. H. Davenport of Cambridge University once said “…in all the records of ancient civilizations there is evidence of some preoccupation with arithmetic over and above the needs of everyday life” (Introduction). The theory of numbers being a...
...Geometric and ArithmeticSequence shows "Survey of Mathematical Methods" and contains solutions on the following problems:
First Problem: question 35 page 230
Second Problem: question 37 page 230
Mathematics  General Mathematics
Week One Written Assignment
Following completion of your readings, complete exercises 35 and 37 in the “Real World Applications” section on page 280 of Mathematics in Our World .
For each exercise,...
...Sequences and Convergence
Let x1 , x2 , ..., xn , ... denote an infinite sequence of elements of a metric space
(S, d). We use {xn }∞
n=1 (or simply {xn }) to denote such a sequence.
Definition 1 Consider x0 ∈ S. We say that the sequence {xn } converges to x0
when n tends to infinity iff: For all > 0, there exists N ∈ N such that for all
n > N , d(xn , x0 ) <
We denote this convergence by lim xn = x0 or simply xn −→ x0 .
n→∞
Example 2...
...Yr12 Test Nov 2009. 1.
Name:________________________
Let Sn be the sum of the first n terms of an arithmeticsequence, whose first three terms are u1, u2 and u3. It is known that S1 = 7, and S2 = 18. (a) (b) (c) Write down u1. Calculate the common difference of the sequence. Calculate u4.
(Total 6 marks)
1
2.
A theatre has 20 rows of seats. There are 15 seats in the first row, 17 seats in the second row, and each successive row of...
...particularly that of the Fibonacci sequence and the Golden Ratio. In Debussy’s Nocturne, composed in 1892, I look into the use of the Fibonacci sequence and the Golden Ratio. Previously it has been noted that composers used the Fibonacci sequence and the Golden Ratio in terms of form, however in my analysis I look into the use of it in terms of notation as well. I will explore how the idea of Sonata form is used along with the Mathematical Model of...
...Job sequence modeling using Genetic Algorithms
Dr.S.N.Sivanandam
Professor & Head
M.Kannan
Senior Lecturer
Department of Computer Science & Engineering,
P.S.G.College of Technology,
Coimbatore641 004
Abstract
This paper presents a Genetic algorithm (GA) based procedure for finding an optimum job sequence for N jobs / M machines problem based on minimum elapsed time. The search space is so large that the Genetic algorithms outperform the...