# What is the next term in the pattern: .1, 1/2, 1/4, 1/8, 1/16..:?

Jul 28, 2016

$\frac{1}{32}$ seems most likely.

#### Explanation:

This appears to be the geometric series $\frac{1}{2} ^ n$ starting at $n = 0$.

Another way to write it would be:
${\sum}_{n = 0}^{i} \frac{1}{2} ^ n$

In your question, $i = 4$ and you are asking for the value at $i = 5$.

The answer is simply evaluated by taking:
$\frac{1}{2} ^ 5 = \frac{1}{32}$

Or alternatively by following the pattern from your already given series values:
$\frac{1}{16} \cdot \frac{1}{2} = \frac{1}{32}$