Question 58
Sequence $\{a_n\}$ satisfies $a_1 = a_2 = a_3$. Let
$$
b_n = a_n + a_{n+1} + a_{n+2} \quad (n \in \mathbb{N}_+).
$$
If $\{b_n\}$ is a geometric sequence with common ratio $3$, find the value of $a_{100}$.
$$
b_n = a_n + a_{n+1} + a_{n+2} \quad (n \in \mathbb{N}_+).
$$
If $\{b_n\}$ is a geometric sequence with common ratio $3$, find the value of $a_{100}$.