1. The problem is to understand the sequence defined by $Y[n] = x[4n+1]$. 2. This means that the sequence $Y$ at index $n$ takes the value of the sequence $x$ at index $4n+1$. 3. The formula used here is a sampling or subsequence extraction formula, where you select elements from $x$ at positions that are multiples of 4 plus 1. 4. For example, when $n=0$, $Y[0] = x[1]$; when $n=1$, $Y[1] = x[5]$; when $n=2$, $Y[2] = x[9]$, and so on. 5. This operation effectively downsamples the sequence $x$ by a factor of 4, starting at index 1. 6. To find any term $Y[n]$, just plug in the value of $n$ into $4n+1$ and find the corresponding term in $x$. Final answer: $Y[n] = x[4n+1]$ defines a subsequence of $x$ taking every 4th element starting from index 1.