Question

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

Answer 1

`1/32` seems most likely.

Explanation:

This appears to be the geometric series `1/2^n` starting at `n=0`.

Another way to write it would be:
`sum_(n=0)^i 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:
`1/2^5 = 1/32`

Or alternatively by following the pattern from your already given series values:
`1/16 * 1/2 = 1/32`