Difference between revisions of "Arithmetic sequence"

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==Definition==
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An arithmetic sequence is a sequence of numbers that increaces a fixed amount in each term.  For an example: 4, 7, 10, 13, 16, ... is an arithmetic sequence because each term is three more than the previous term. In this case, 3 is called the ''common difference''. A more formal definition is: a sequence <math>a_n</math> with fixed <math>a_1</math> that follows the recurrence relation: <math>a_n = a_{n-1} + r</math>, where <math>r</math> is the common difference.
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==Sums of Arithmetic Sequences==
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The sum of any terms in an arithmetic sequence is given by the average of the first term and the last term, multiplied by the number of terms there are.  For an example,
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<math>\displaystyle 5 + 7 + 9 + 11 + 13 + 15 + 17 = \frac{5+17}{2}*7 = 77</math>
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==See Also==
 
==See Also==
 
[[geometric sequence|Geometric Sequences]]
 
[[geometric sequence|Geometric Sequences]]

Revision as of 04:02, 23 June 2006

Definition

An arithmetic sequence is a sequence of numbers that increaces a fixed amount in each term. For an example: 4, 7, 10, 13, 16, ... is an arithmetic sequence because each term is three more than the previous term. In this case, 3 is called the common difference. A more formal definition is: a sequence $a_n$ with fixed $a_1$ that follows the recurrence relation: $a_n = a_{n-1} + r$, where $r$ is the common difference.

Sums of Arithmetic Sequences

The sum of any terms in an arithmetic sequence is given by the average of the first term and the last term, multiplied by the number of terms there are. For an example,

$\displaystyle 5 + 7 + 9 + 11 + 13 + 15 + 17 = \frac{5+17}{2}*7 = 77$

See Also

Geometric Sequences