Arithmetic and Geometric Sequences and Series

Arithmetic series - find $a_{n}$

$$a_n = a_1 + d(n-1)$$

Arithmetic series - find $S_{n}$

$$S_n = \frac{n}{2}(a_1 + a_n)$$

Geometric series - find $a_{n}$

$$a_n = a_1r^{n-1}$$

Geometric series - find $S_{n}$

$$S_n = \frac{a_1 - a_1r^n}{1 - r}$$

Geometric series - find $S\infty$

$$S_{\infty}=\frac{a_1}{1 - r}$$