# Reach for the Summit - M-S3-A1

Algebra Level 3

Given a positive infinite sequence $\{a_n\}$, $S_n = \displaystyle \sum_{k=1}^{n} a_k$.

If $\forall n \in \mathbb N^+$, the arithmetic mean of $a_n$ and $2$ is equal to the geometric mean of $S_n$ and $2$, then find $a_{2020}$.

Reach for the Summit problem set - Mathematics

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