Difference between revisions of "Arithmetic sequence"
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| + | ==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 <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 03:02, 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 
with fixed 
that follows the recurrence relation: 
, where 
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,
