Difference between revisions of "Arithmetic series"
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is an arithmetic series whose value is 50. | is an arithmetic series whose value is 50. | ||
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To find the sum of an arithmetic sequence, we can write it out in two as so (<math>S</math> is the sum, <math>a</math> is the first term, <math>z</math> is the number of terms, and <math>d</math> is the common difference): | To find the sum of an arithmetic sequence, we can write it out in two as so (<math>S</math> is the sum, <math>a</math> is the first term, <math>z</math> is the number of terms, and <math>d</math> is the common difference): | ||
<cmath> | <cmath> |
Revision as of 19:32, 19 September 2015
An arithmetic series is a sum of consecutive terms in an arithmetic sequence. For instance,
is an arithmetic series whose value is 50.
Contents
[hide]Formula
To find the sum of an arithmetic sequence, we can write it out in two as so ( is the sum, is the first term, is the number of terms, and is the common difference): Flipping the right side of the equation we get
Now, adding the above two equations vertically, we get
This equals , so the sum is .
Problems
Introductory Problems
Intermediate Problems
Olympiad Problem
See also
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