Category:Examples of Sum of Arithmetic Sequence

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This category contains examples of use of Sum of Arithmetic Sequence.

Let $\sequence {a_k}$ be an arithmetic sequence defined as:

$a_k = a + k d$ for $n = 0, 1, 2, \ldots, n - 1$


Then its closed-form expression is:

\(\ds \sum_{k \mathop = 0}^{n - 1} \paren {a + k d}\) \(=\) \(\ds n \paren {a + \frac {n - 1} 2 d}\)
\(\ds \) \(=\) \(\ds \frac {n \paren {a + l} } 2\) where $l$ is the last term of $\sequence {a_k}$