That finite sequence we can just add up, using 16 as a common denominator

They probably want you to use the formula

That's the special case of a geometric series where the first term is one. If it's not we multiply the answer by the first term.
In our example, r=1/2 and n=5, meaning five terms.

Same answer, math works!
If the question was asking about the infinite geometric series, that's just a little bigger: