SEAMO 2023 — Paper E — Grade 9–10 Question 14

Question 14

The first $n$ terms of $\{a_n\}$ sum to $S_n=2a_n-1$. A sequence $\{b_n\}$ satisfies $b_1=3$ and $b_{k+1}=b_k+a_k$ for $k\ge1$. Find the sum of the first $8$ terms of $\{b_n\}$.

$270$
$271$
$272$
$529$
$530$