In three dimensions, a multivector consists of a scalar, a vector, a bivector and a tri-vector. Is there a term that generalizes these names? For example, in an $n$-dimensional space, can I use the terminology $k$-vector (where $0\leq k\leq n$) to refer to the different scalar and vector types, such that a 0-vector is a scalar, a 1-vector is a vector, a 2-vector is a bivector and a 3-vector is a trivector? I haven't found any such name generalization, but it seems to me like it would be very useful (kind of like how a face of an $n$-polytope can be referred to as a $k$-face, where $0\leq k\leq n$ and $k$ is the dimensionality of the face).
Edit: I found the answer to my own question. They can indeed be called $k$-vectors.
Scalars, vectors, bivectors and trivectors can indeed collectively be referred to as $k$-vectors.