What is the name of this mathematical object

Question

While i was programming i incountered the following: The set of all subsequences of $A$ that are in the form of $(a_n,a_{n+1},...,a_{n+k}),\ k>0$. I wanted to know if this kind of subsequences has a name, and if they are useful.

Answer 1

Such objects are called $k+1$-tuples. (For example, if $k=1$ we call them $2$-tuples. It's more common to refer to $n$-tuples viz. $k=n-1$, although that's inconvenient given how you've parameterised the indices.) Construed as subsequences, I suppose you could call it a $k+1$-tuple subsequence, or (if you needn't specify the value of $k$) finite consecutive subsequences. If there is another name for them, your readership probably wouldn't know it, so it's worth sticking with familiar terms.