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What is the common difference in the context of an arithmetic sequence?

The difference between consecutive terms

In an arithmetic sequence, the common difference refers to the constant value that is added to each term to get the next term. This means that if you take any term in the sequence and subtract the term that precedes it, the result will always be the same for all consecutive terms. This consistent difference is what characterizes an arithmetic sequence, making it predictable and structured.

The importance of the common difference lies in its ability to define the entire sequence. For instance, if the first term is known and the common difference is determined, one can generate all subsequent terms of the sequence. Understanding this concept is fundamental in recognizing patterns within arithmetic sequences and solving related problems effectively.

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The sum of the first and last terms

The average of the sequence

The first term of the sequence

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