Number sequence as geometric sequence

Question

In a number sequence, I've figured the $n^{th}$ element can be written as $10^{2-n}$.

I'm now trying to come up with a formula that describes the sum of this sequence for a given $n$. I've been looking at the geometric sequence, but I'm not sure how connect it.

Answer 1

Hint: We have $10^{2-n}=10^2\cdot 10^{-n}=10^2\cdot(10^{-1})^n$ and $$\sum_{k=0}^n x^k=\frac{1-x^{n+1}}{1-x}.$$

Answer 2

If it is $10^{2-n}$ then, the initial term is $10$ and common ratio is $\frac 1{10}$, Now, can you get it?