Question 15
A sequence $\{a_i\}_{i=1}^{\infty}$ is called a good sequence if $\dfrac{S_{2n}}{S_n}$ is a constant for all $n\ge1$, where $S_k$ denotes the sum $a_1+a_2+\cdots+a_k$. Suppose it is known that the sequence $\{a_i\}_{i=1}^{\infty}$ is a good sequence that follows an arithmetic progression. Determine $a_{2020}$ if $a_1=1\ne a_2$.