Number sequences can be used as a tool to determine your numerical reasoning skill. These types of sequences are often found in IQ Tests, psychometric assessments and aptitude tests and practicing these will improve your numerical reasoning ability. Number sequences tests are a type of numerical aptitude test which require you to find the missing number in a sequence. This missing number may be at the beginning or middle but is usually at the end. Number sequences is a collective term for a sequence of numbers that can be divided into integer and rational sequences.

Integer Number Sequences

Integers are whole numbers. An integer number could be 0, 1, 2, etc. and these positive integer numbers are called natural numbers. Their counterparts are of course negative integers and are negative whole numbers, such as -3, -2 and -1. Integer sequences are therefore sequences based on whole numbers, both positive and negative and including zero, for instance:

-1, 1, 3, 5, 7, …

The number sequence can be specified explicitly by giving a formula for its nth term. The formula for this sequence is “2n−1″ for the nth term and can be called an explicit definition. Explicit meaning that you can chose any integer number for the letter “n” in the formula and it will generate a number in the sequence, for instance: n=3 will generate 2*3-1 = 5 as shown in the example.

An implicit number sequence is given by a relationship between its terms. For example, the Fibonacci sequence

0, 1, 1, 2, 3, 5, 8, 13, …

This number sequence is formed by starting with 0 and 1 and then adding any two consecutive terms to obtain the next one. This relationship is called an implicit description, since you cannot define this in such an easy formula with only one variable as in an explicit definition.

Rational Number Sequences

Unlike integers, rational numbers are numbers which can be written as a fraction where numerator and...

...SEQUENCE
* In mathematics, informally speaking, a sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements, or terms). The number of ordered elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Most precisely, asequence can be defined as a function whose domain is a countable totally ordered set, such as the natural numbers.
* For example, {M, A, R, Y} is a sequence of letters with the letter 'M' first and 'Y' last. This sequence differs from {A, R, M, Y}. Also, the sequence {1, 1, 2, 3, 5, 8}, which contains the number 1 at two different positions, is a valid sequence. Sequences can be finite, as in this example, or infinite, such as the sequence of all even positive integers {2, 4, 6,...}. Finite sequences are sometimes known as strings or words and infinite sequences as streams. The empty sequence { } is included in most notions of sequence, but may be excluded depending on the context.
ARITHMETIC SEQUENCE
* A sequence such as 1, 5, 9, 13, 17 or 12, 7, 2, –3, –8, –13, –18 which has...

...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+ (n-1) d
a125=100+ (125-1) (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 90-foot 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(rn-1)
a10=525(1.05-9)
a10=525(1.551328216)
a10=814.4473134
The balance in the savings account at the end of 10 years will be $814.44.
I...

...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 Consider the sequence {xn } in R, defined by xn = n1 . Then xn −→
0.
The way to prove this is standard: fix > 0. We need to find N ∈ N such that
for all n > N , d(xn , 0) < . We have d(xn , 0) = |xn − 0| = | n1 |
So it is enough that n1 < , or equivalently n > 1 . So choosing N > 1 we know
that for all n > N , d(xn , 0) < .
The fact that we define the concept of convergence does not imply that every
sequence converges. This is illustrated in the next two examples. Let’s begin
with a remark about what it means for a sequence {xn } not to converge to x0 .
Remark: To know what the non-convergence of a sequence means, we need
to write the negation of the definition of convergence. That reduces to: There
exists > 0, such that for all N ∈ N, there exists n > N such that d(xn , x0 ) ≥ .
For the ones of you familiar with propositional logic, notice that convergence to
x0 can be written as
(∀ > 0)(∃N ∈ N)(∀n > N )d(xn , x0 ) <
Its negation...

...
This work MAT 126 Week 1 Assignment - Geometric and Arithmetic Sequence 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, specify whether it involves an arithmetic sequence or a geometric sequence and use the proper formulas where applicable . Format your math work as shown in the Week One Assignment Guide and be concise in your reasoning. Plan the logic necessary to complete the exercise before you begin writing. For an example of the math required for this assignment, please review the Week One Assignment Guide .
The assignment must include ( a ) all math work required to answer the problems as well as ( b ) introduction and conclusion paragraphs.
Your introduction should include three to five sentences of general information about the topic at hand.
The body must contain a restatement of the problems and all math work, including the steps and formulas used to solve the problems.
Your conclusion must comprise a summary of the problems and the reason you selected a particular method to solve them. It would also be appropriate to...

...we were to keep going month by month, the sequence formed would be 1,1,2,3,5,8,13,21 and so on. From here we notice that each new term is the sum of the previous two terms. The set of numbers is defined as the Fibonacci sequence. Mathematically speaking, this sequence is represented as:
The Fibonacci sequence has a plethora of applications in art and in nature. One frequent finding in nature involves the use of an even more powerful result of the Fibonacci sequence: phi and the golden ratio. The following is an example of what I will later discuss: the golden spiral.
Figure 2: The arrangement of the whorls on a pine cone follows a sequence of Fibonacci numbers.
The following example is just one of the numerous examples of the fascination applications found within the Fibonacci sequence in nature. Now, we turn to one of the most fundamental concepts of the Fibonacci sequence: the golden ratio.
Consider the ratio of the Fibonacci numbers (1,1,2,3,5,8, )
As, the sequence progresses, we notice that the sequence seems to converge and approach a number. The question is what exactly is that number?
Answer:
One of the most interesting and frequent applications of phi is that of the golden rectangle. The golden rectangle is created in a way...

...In mathematics, a real number is a value that represents a quantity along a continuous line. The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers such as √2 (1.41421356... the square root of two, an irrational algebraic number) and π (3.14159265..., a transcendental number). Real numbers can be thought of as points on an infinitely long line called the number line or real line, where the points corresponding to integers are equally spaced. Any real number can be determined by a possibly infinite decimal representation such as that of 8.632, where each consecutive digit is measured in units one tenth the size of the previous one. The real line can be thought of as a part of the complex plane, and correspondingly, complex numbers include real numbers as a special case.
These descriptions of the real numbers are not sufficiently rigorous by the modern standards of pure mathematics. The discovery of a suitably rigorous definition of the real numbers — indeed, the realization that a better definition was needed — was one of the most important developments of 19th century mathematics. The currently standard axiomatic definition is that real numbers form the unique complete totally ordered field (R,+,·,<), up...

...notation (see the table for its representation in some other bases). The constant is also known as Archimedes Constant, although this name is rather uncommon in modern, western, English-speaking contexts. Many formulae from mathematics, science, and engineering involve π, which is one of the most important mathematical and physical constants.[5]
π is an irrational number, which means that its value cannot be expressed exactly as a fraction m/n, where m and n are integers. Consequently, its decimal representation never ends or repeats. It is also a transcendental number, which implies, among other things, that no finite sequence of algebraic operations on integers (powers, roots, sums, etc.) can be equal to its value; proving this was a late achievement in mathematical history and a significant result of 19th century German mathematics. Throughout the history of mathematics, there has been much effort to determine π more accurately and to understand its nature; fascination with the number has even carried over into non-mathematical culture.
The Greek letter π, often spelled out pi in text, was adopted for the number from the Greek word for perimeter "περίμετρος", first by William Jones in 1707, and popularized by Leonhard Euler in 1737.
Are you aware of the fact the first 100 decimal digits of pi had already been calculated by the year 1701? Read on to know more.
And he made a molten sea, ten cubits...

... 3 is a number, numeral, and glyph. It is the natural number following 2 and preceding 4.
In mathematics
Three is approximately π when doing rapid engineering guesses or estimates. The same is true if one wants a rough-and-ready estimate of e, which is actually approximately 2.71828.
Three is the first odd prime number, and the second smallest prime. It is both the first Fermat prime and the first Mersenne prime, the onlynumber that is both, as well as the first lucky prime. However, it is the second Sophie Germain prime, the second Mersenne prime exponent, the second factorial prime, the second Lucas prime, the second Stern prime.
Three is the first unique prime due to the properties of its reciprocal.
Three is the aliquot sum of 4.
Three is the third Heegner number.
According to Pythagoras and the Pythagorean school, the number 3, which they called triad, is the noblest of all digits, as it is the only number to equal the sum of all the terms below it, and the only number whose sum with those below equals the product of them and itself.
Three is the second triangular number and it is the only prime triangular number. Three is the only prime which is one less than a perfect square. Any other number which is n2 − 1 for some integer n is not prime, since it is . This is true for 3 as well, but in its...