algorithms and the sequencing of numbers given a value
I don't see an algorithm in your answer. Also, I doubt that if you convert your sequence of steps into an algorithm, then it will produce the correct answer for $n=0,\ldots,5$.
From the given examples, you can see that the first number in the sequence is always $3n$, and from then on the numbers increase by $2$ each time (as you mention; but then in your &quot;algorithm&quot; they decrease by $2$ each time), and in total there are $2(n+1)$ of them (you can see this since the length of the sequence increases by $2$ each time).
How do we convert this into an algorithm? An algorithm is a recipe that prints the sequence for every value of $n$, not for the particular value $n=6$. Also, it should reproduce the given sequences for $n = 0,\ldots,5$.
Your question makes me doubt that the lecturer has explained the concept of &quot;algorithm&quot;, so instead, try to write a function in your favorite programming languages that given $n$, prints the sequence corresponding to $n$. Code is just a formal way of presenting an algorithm.