1. This isn't a geometric sequence. You can factorise out 1/2 so that it becomes

2. This one is a geometric sequence.

The general form for a geometric sequence is

Where a is the first term and r is the common ratio

Each term is half of the previous so the common ratio is 1/2, and the first term is 1/2.

3. Find the first term a_{1}

Find the common ratio which is for all values of n

The fifth partial sum is

Likewise, the nth partial sum is

The sum of the first n terms is equal to

To find the fifth partial sum you could find the first 5 terms and add them up, or use that formula.