Let $X$~ $Geo(p)$. define $Y = \lceil X/2 \rceil$. what is the distribution of $Y$?

Question

I have a question in discrete probability space:

Let $X$~ $Geo(p)$. define $Y = \lceil X/2 \rceil$. what is the distribution of $Y$?

$P(Y=n) = P(\lceil X/2 \rceil = n) .. $ not sure how to find it.

Answer 1

$P(Y=n) = P(X = 2n-1) + P( X=2n)$.