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How do I find the partial sum of an arithmetic sequence?

1 Answer

Aug 5, 2018

$S_{n} = \frac{n}{2} \cdot (2 a + (n - 1) d)$ $color(purple)(S_n = n/2 * (2a + (n-1)d)$

Explanation:

First term is a, common difference is d

$n^{t h}$ $n^(th)$ $t e r m$ $term$ $a_{n} = a + (n - 1) \cdot d$ $a_n = a + (n-1) * d$

Partial sum of an arithmetic sequence is given by

$S_{n} = \frac{n}{2} \cdot (a + a_{n}) = \frac{n}{2} \cdot (a + (a + (n - 1) \cdot d)$ $S_n = n / 2 * (a + a_n) = n/2 * (a + (a + (n-1) * d)$

$S_{n} = \frac{n}{2} \cdot (2 a + (n - 1) d)$ $color(purple)(S_n = n/2 * (2a + (n-1)d)$

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