\begin{definition}[Definition:Linear Combination/Sequence]
Let $M$ be an $R$-module.
Let $\sequence {a_n} := \sequence {a_j}_{1 \mathop \le j \mathop \le n}$ be a sequence of elements of $M$ of length $n$.
An element $b \in M$ is a '''linear combination''' of $\sequence {a_n}$ {{iff}}:
:$\ds \exists \sequence {\lambda_n} \subseteq R: b = \sum_{k \mathop = 1}^n \lambda_k a_k$
\end{definition}