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 a1
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.