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Topic: Arithmetic series


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  NationMaster - Encyclopedia: Arithmetic series
In mathematics, an arithmetic series is the sum of the components of an arithmetic progression.
Series may be finite, or infinite; in the first case they may be handled with elementary algebra, but infinite series require tools from mathematical analysis if they are to be applied in anything more than a tentative way.
Series for the expansion of sines and cosines, of multiple arcs in powers of the sine and cosine of the arc had been treated by Jakob Bernoulli (1702) and his brother Johann Bernoulli (1701) and still earlier by Viète.
www.nationmaster.com /encyclopedia/Arithmetic-series   (426 words)

  
 Draw Sizer - Arithmetic Progression
This utility employs arithmetic progression to compute drawer face heights by progressively adding a fixed increment to successive drawers beginning with the top drawer.
With arithmetic progression, the heights of successive drawer faces differ by a constant amount or "increment".
Arithmetic progression is fairly straightforward, especially when you already have values in mind for the height of the top drawer, the number of drawers, and the height increment.
www.woodbin.com /calcs/drawsizer_arithmetic.htm   (346 words)

  
 MathComplete.com - Sequence and Series - Tutorial   (Site not responding. Last check: 2007-09-09)
A series is formed by the sum of the terms of a sequence.
Arithmetic series is a sum of a number each of which, after the first, is obtained by adding to the preceding number a constant number called the common difference.
Geometric series is a sum of a number each of which, after the first, is obtained by multiplying the preceding number by a constant number called common ratio.
www.mathcomplete.com /tutorial/sequence/default.asp?Pg=2   (271 words)

  
 PlanetMath: arithmetic-geometric series
It is well known that a finite geometric series is given by
This last result giving the sum of a converging arithmetic-geometric series may be, naturally, obtained also from the sum formula of the converging geometric series, i.e.
This is version 3 of arithmetic-geometric series, born on 2006-06-26, modified 2006-06-27.
planetmath.org /encyclopedia/ArithmeticGeometricSeries.html   (161 words)

  
 Algebra II Recipe: Arithmetic Series   (Site not responding. Last check: 2007-09-09)
arithmetic series - the expression formed by adding the terms of an arithmetic sequence
Finding the sum of the first n terms of an arithmetic sequence
Consider the arithmetic series 4 + 7 + 10 + 13 + 16 + 19 + …
www.algebralab.org /studyaids/studyaid.aspx?file=Algebra2_11-2.xml   (105 words)

  
 Arithmetic Progressions
An arithmetic progression is a sequence in which each term (except the first term) is obtained from the previous term by adding a constant known as the common difference.
An arithmetic series is formed by the addition of the terms in an arithmetic progression.
He counted 101 terms in the series, of which 50 is the middle term.
library.thinkquest.org /C0110248/algebra/apgparith.htm   (264 words)

  
 Arithmetic Series   (Site not responding. Last check: 2007-09-09)
One common type of series is the arithmetic series (also called an arithmetic progression).
Each new term in an arithmetic series is the previous term plus a given number.
To specify which series we mean, we need to know one more piece of information: the value of the first term (usually called "a").
www.ucl.ac.uk /Mathematics/geomath/level2/series/ser2.html   (224 words)

  
 Arithmetic Series | World of Mathematics
There is a formula for computing the sum of a finite arithmetic series which is useful when the number of terms is large.
The sum 1+2+3+4+...+97+98+99+100 is an arithmetic series with common difference 1.
Notice that 101 is the sum of the first and last terms of the series and 50 is the number of pairs or 100/2.
www.bookrags.com /sciences/mathematics/arithmetic-series-wom.html   (341 words)

  
 Complete 20 Volume Set - Ray's Arithmetic
This complete series will take your student from Primary Arithmetic to Ray's Differential and Integral Calculus and beyond.
Ray's Arithmetics students learn arithmetic, increase their reading comprehension skills, and learn to think rather than plod through page after page of addition or subtraction problems with a one line direction at the top of each page.
Teachers every-where, throughout the length and breadth of the land, are familiar with it's pages, and millions of pupils have gained their arithmetic knowledge from the study of it's principles.
www.raysarithmetic.com   (1017 words)

  
 Quandaries & Queries at Math Central
The first term in an arihmetic series is 25 and the 3rd term is 19.
This is the question: The 5th term in an arithmetic sequence is 1/2, and the 20th term is 7/8.
The sum of the first ten terms of an arithmetic series is 100 and the first term is 1.
mathcentral.uregina.ca /QandQ/topics/arithmetic   (2498 words)

  
 Discrete Algebra - Sequences and Series - Arithmetic Progression
An arithmetic progression is a sequence in which each term (after the first) is determined by adding a constant to the preceding term.
This constant is called the common difference of the arithmetic progression.
The 6th to 10th terms of this arithmetic progression are
library.thinkquest.org /10030/11snsap.htm   (241 words)

  
 BBC Education - AS Guru - Maths - Pure - Sequences and Series - Arithmetic Sequences
This is one of the simplest arithmetic series.
terms of the arithmetic series with first term 1 and common difference 1.
Notice that the first and last terms, the second and next to last terms, the third and second to last terms all form pairs which add up to the same value.
www.bbc.co.uk /education/asguru/maths/13pure/03sequences/17arthimetic/principles.shtml   (503 words)

  
 PlanetMath: arithmetic series
Now we express the sum of the sequence by developing the series forward and we have:
This is version 7 of arithmetic series, born on 2006-10-04, modified 2006-10-07.
(Sequences, series, summability :: Convergence and divergence of infinite limiting processes :: Convergence and divergence of series and sequences)
planetmath.org /encyclopedia/ArithmeticSeries.html   (118 words)

  
 SparkNotes: Sequences and Series: Terms and Formulae
Arithmetic Sequence - A sequence in which each term is a constant amount greater or less than the previous term.
Divergent Series - A series whose limit as n→∞ is either ∞ or - ∞.
Finite Series - A series which is defined only for positive integers less than or equal to a certain given integer.
www.sparknotes.com /math/precalc/sequencesandseries/terms.html   (388 words)

  
 The 'Quilting' Lesson - Arithmetic Vs. Geometric Series
This is a lesson idea which, oddly enough, could be used either in a high school mathematics class, to explore the differences between arithmetic and geometric series, or as a lesson in a leadership/teaching seminar.
This is an arithmetic progression, and if you are using this lesson in a math class, you should point that out.
This is a good exercise for a math class because, like the Chess Board Problem, it gives a simple but obvious demonstration of how a geometric series can "explode" in comparison to an arithmetic series.
www.articlesforeducators.com /dir/mathematics/sequences_series/quilting_lesson.asp   (681 words)

  
 Arithmetic Series
An arithmetic series is the sum of an arithmetic sequence.
A geometric series is the sum of a geometric sequence.
There are other types of series, but you're unlikely to work with them until you're in calculus.
www.purplemath.com /modules/series4.htm   (324 words)

  
 Arithmetic and Geometric Sequences
The two simplest sequences to work with are arithmetic and geometric sequences.
An arithmetic sequence goes from one term to the next by always adding (or subtracting) the same value.
Since arithmetic and geometric sequences are so nice and regular, they have formulas.
www.purplemath.com /modules/series3.htm   (398 words)

  
 [No title]
If NEITHER of these conditions is satisfied, then obviously it is neither arithmetic nor geometric. FYI, there are MANY MANY different type of sequences and series...
You do not need to "do the difference" becuse you already know that the sequence is arithmetic, so it can’t be geometric. As to why we call it a "partial sum"; the reason is that all sequences are "infinite".
So this is an infinite geometric sequence. If you try to sum the "first 13 terms" or some such thing, then it would be called a "partial sum".
spot.pcc.edu /~jtobin/Arithmetic_and_Geometric_Sequences.doc   (226 words)

  
 MathComplete.com - Sequence and Series - Tutorial   (Site not responding. Last check: 2007-09-09)
Arithmetic sequence is a sequence of a number each of which, after the first, is obtained by adding to the preceding number a constant number called the common difference.
Let's take a following sequence, we may quickly check is this the arithmetic sequence.
This is arithmetic sequence because we have a common difference d = 3
www.mathcomplete.com /tutorial/sequence/default.asp?pg=1   (283 words)

  
 My Information   (Site not responding. Last check: 2007-09-09)
Example: An arithmetic sequence has 6 as its first tem and a common difference of -2.
n is the number of terms in the series.
Example: An arithmetic series has 18 terms, a common difference of 3 and the first term of the series is -9.
www.angelfire.com /va3/numbersandalgebra/Arithmetic.html   (197 words)

  
 Basic Math - Ray's Arithmetic
This CD-ROM is Disk 1 of the Ray's Arithmetic series.
The Dubbs book was published a decade after the others, but it is an actual part of the series and good workbook (with answers in the back) and it is suggested that the student work all the problems in both books.
Higher Arithmetic is a challenging book which covers a lot of material.
www.raysarithmetic.com /view/raysarithmetic/s144p1489.htm   (977 words)

  
 Geometric Sequences and Series   (Site not responding. Last check: 2007-09-09)
We can do this by finding the first few terms of the series and determining if the series is arithmetic or geometric.
Since the number at the top of the sigma or summation symbol is an infinity, we need to do two thing: determine if this series is geometric and if it is, determine if the common ratio has an absolute value less than 1.
Let's start by determining if the series is geometric by finding the first few terms of the series.
fym.asu.edu /~fym/mat117-internet/sequences_and_series_notes/geometric-sequences-and-series/Geometric_Sequences_and_Series.html   (1712 words)

  
 Summing an arithmetic series   (Site not responding. Last check: 2007-09-09)
Now we're going to add those two series together (we know they have the same number of terms because it's just the same series written two different ways round).
The result must be twice the sum we're looking for, since both series separately add up to that sum.
And we've got N pairs of terms (since that's the number of terms in the series) so the total sum is Nx(2a+(N-1)d).
www.ucl.ac.uk /Mathematics/geomath/level2/series/ser5.html   (231 words)

  
 Arithmetic Sequences and Series
Suppose that the 13th term of an arithmetic sequence is 46 and the fourth term is 100.
is an arithmetic sequence then the sum of the sequence is
Suppose that the sum of the first 18 terms of an arithmetic sequence is -45 and
www.ltcconline.net /greenl/Courses/103B/seqSeries/ARITSEQ.HTM   (404 words)

  
 7.2 - Arithmetic Sequences   (Site not responding. Last check: 2007-09-09)
An arithmetic sequence is a sequence in which the difference between consecutive terms is constant.
If the difference in consecutive terms is not constant, then the sequence is not arithmetic.
There is an easy way to calculate the sum of an arithmetic series.
www.richland.edu /james/lecture/m116/sequences/arithmetic.html   (613 words)

  
 Arithmetic Sequences
An arithmetic sequence is nothing more than a linear function with the specific domain of the natural numbers.
The arithmetic family of sequences and their associated series one of the easiest to work with.
The average of the first and last terms is undefined since we are using an infinite value in the process.
fym.la.asu.edu /~tturner/MAT_117_online/SequenceAndSeries/Arithmetic_Sequences.htm   (742 words)

  
 The Chess Problem - Teaching Arithmetic and Geometric Series
The Chess Problem is a silly story that helps students see the difference between arithmetic series and geometric series.
The king of Loolooland was under attack by bandits in the Looloo Forest, and was rescued by the brave Sir Lagbehind, a knight of the Rhomboid Table.
The first is an arithmetic series, and the second is a geometric series.
www.articlesforeducators.com /dir/mathematics/sequences_series/chess_problem.asp   (525 words)

  
 Hotmath Solution Finder
Determine the next four terms in the arithmetic sequence 9 19, 29, 39,....
Find the arithmetic mean of the given pair of numbers:
List all the terms in the given arithmetic series.
hotmath.com /help/gt/genericalg2/section_9_2.html   (216 words)

  
 Arithmetic Series   (Site not responding. Last check: 2007-09-09)
A series that is formed by adding a constant on to each term, is called an Arithmetic Series.
Therefore, the sum of an arithmetic series is
When a question is given in this form, you first need to write out a few terms, to establish the nature of the series.
www.mathsyear2000.org /alevel/pure/purtutserari.htm   (186 words)

  
 Arithmetic series - Definition, explanation
Printable arithmetic worksheets based on the 52 skill levels of the Math Skill Builders series are updated weekly for free download.
Number theory, representation theory, and arithmetic geometry: especially L-functions, Eisenstein series, theta series, Shimura varieties, intersection theory, and elliptic curves.
Number theory, representation theory, and arithmetic geometry: especially L-functions, Eisenstein series, theta series, Shimura varieties, intersection theory, and...
www.calsky.com /lexikon/en/txt/a/ar/arithmetic_series.php   (472 words)

  
 Arithmetic Mean
A mathematical representation of the typical value of a series of numbers, computed as the sum of all the numbers in the series divided by the count of all numbers in the series.
Arithmetic mean is commonly referred to as "average" or simply as "mean".
If during the five-day week the stock closed at $14.50, $14.80, $15.20, $15.50, and then $14.00, its arithmetic mean closing price would be equal to the sum of the five numbers ($74.00) divided by five, or $14.80.
www.investopedia.com /terms/a/arithmeticmean.asp   (291 words)

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