SEAMO 2027 - Paper E - SET 02 - Self-study Question 8

The sum of the first $n$ terms of $\{a_n\}$ is $S_n=2a_n-1$, for $n=1,2,3,\ldots$. The sequence $\{b_n\}$ satisfies $b_1=3$ and $b_{k+1}=b_k+a_k$, for $k=1,2,3,\ldots$. Find the sum of the first $n$ terms of $\{b_n\}$ when $n=8$.