Question

What is the next term in the pattern:$1,\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{16}....?$

Answer 1

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:

$\frac{1}{16}.\frac{1}{2}=\frac{1}{32}$