Are parts of a pseudorandom string also a pseudorandom string? I am working on an exercise that encrypts a message using only the first $n$ bits of a pseudorandom generator's output $G(k)$, i.e. $F_k(m) := G(k)_{0...n−1} \oplus m$.

$k$ is chosen uniformly at random and $k, m \in \{0, 1\}^n$. 
My task is to decide whether an encryption scheme based on $F_k$ can be secure against a ciphertext-only attack, a CPA attack and whether it's indistinguishable.

My idea was that, if $G(k)_{0...n−1}$ is still a pseudorandom string, the exercise reduces to the case of using the whole output of $G(k)$. Then the scheme would be secure against a ciphertext-only attack and indistinguishable, but not secure against CPA attacks since it's a deterministic scheme.

My problem is that I couldn't find out, whether $G(k)_{0...n−1}$ can be treated exactly like the entire output of $G(k)$. Furthermore, I am not sure whether my intuition about solving the exercise is right. I would appreciate any hints!
If you have a stream, $s$, of $n$ bits that is computationally indistinguishable from random, then any truncation of that $n$ bit string must also be indistinguishable from random.

The proof of this is straightforward. If $s$ was computationally indistinguishable from random, but some truncation of $s$ was not then we could distinguish the larger sequence from random by enumerating all possible truncations of $s$ and testing them against the distinguisher.

If the distinguisher identifies that any truncation is not random, then this demonstrates $s$ is not random. It acts as a distinguisher on $s$. Obviously, that is a contradiction.