Category:Examples of Sum of Arithmetic Progression

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

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

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


Then its closed-form expression is:

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