Category:Examples of Sum of Arithmetic Sequence
Jump to navigation
Jump to search
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 $k = 0, 1, 2, \ldots, n - 1$
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 $\sequence {a_k}$ |
Pages in category "Examples of Sum of Arithmetic Sequence"
The following 6 pages are in this category, out of 6 total.