15 lines
894 B
Markdown
15 lines
894 B
Markdown
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---
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title: Arithmetic Sequence
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---
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## Arithmetic Sequence
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An arithmetic sequence, or arithmetic progression, is a sequence of numbers where the difference between each consecutive number is the same.
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If n is the placement of some term in the sequence (e.g. 1, 2, 3...), d is the difference between each consecutive term, k is the first the placement of the first known term of the sequence (e.g. if you know the first term, then k = 1), a<sub>k</sub> is the value of the k<sup>th</sup> term in the sequence (i.e. the value at term number k), and a<sub>n</sub> is the value of the n<sup>th</sup> term in the sequence (i.e. the value at term number n), then the equation for an arithmetic sequence is this<sup>1</sup>:
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a<sub>n</sub> = a<sub>k</sub> + d(n - k)
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### Sources
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1. ["Arithmetic Progressions." *Brilliant.org*. October 1, 2018.](https://brilliant.org/wiki/arithmetic-progressions/)
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