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# Def/Sequence of differences

Definition of Sequence of differences: Suppose that $(a_i)$ is a Def/Sequence of numbers, indexed by $i \in \NN$ or $i \in \ZZ$. The values $a_i$ may be integers or real numbers, or most generally, elements of any abelian group.

The sequence of differences, or difference sequence, of $(a_i)$ is the sequence denoted $(a_i')$, defined by: $$a_i' = a_{i+1} - a_i,$$ for all $i$ in the indexing set ($\NN$ or $\ZZ$).

## Logical Connections

This definition logically relies on the following definitions and statements: Def/Sequence

The following statements and definitions logically rely on the material of this page: Def/Arithmetic progression, Def/Quadratic sequence, and State/Values in the range topograph adjacent to a given face form a quadratic sequence

To visualize the logical connections between this definition and other items of mathematical knowledge, you can visit any of the following clusters, and click the "Visualize" tab:

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