or

$S_n = \frac{n[2a_1 + (n-1)d]}{2}$

where $n$ = number of terms

Geometric Series

Sum of a geometric sequence: $S_n = a_1 \cdot \frac{1 - r^n}{1 - r}$

(when $r \neq 1$)

Infinite Geometric Series

If $|r| < 1$, the infinite series has a sum: $S = \frac{a_1}{1 - r}$

Example: $1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ...$

$S = \frac{1}{1 - \frac{1}{2}} = \frac{1}{\frac{1}{2}} = 2$

Sigma Notation

$\sum_{i=1}^{n} a_i = a_1 + a_2 + a_3 + ... + a_n$

Read as: "the sum from $i = 1$ to $n$ of $a_i$"

Since $|r| = \frac{1}{2} < 1$, the series converges.

Use the formula: $S = \frac{a_1}{1 - r}$

$S = \frac{8}{1 - \frac{1}{2}}$ $= \frac{8}{\frac{1}{2}}$ $= 16$

Answer: $16$