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

Aug 5, 2018

color(purple)(S_n = n/2 * (2a + (n-1)d)

#### Explanation:

First term is a, common difference is d

${n}^{t h}$ $t e r m$ ${a}_{n} = a + \left(n - 1\right) \cdot d$

Partial sum of an arithmetic sequence is given by

S_n = n / 2 * (a + a_n) = n/2 * (a + (a + (n-1) * d)

color(purple)(S_n = n/2 * (2a + (n-1)d)