Q:

Proof that a specific bounded sequence converges?

$(a_n)$ is a bounded sequence such that $$\lim_{n\to\infty}(a_{2^n}-3a_n)=0$$
Prove that $(a_n)$ converges and determine the limit.
I haven't got a clue of what to do here. I've been told I could watch accumulation points of the sequence but honestly I don't understand how I should proceed. Any kind of hint would be really helpful.
Thanks in advance!

A:

Hint: If $L$ is a limit point then $3L$ is also a limit point. Since sequence is bounded $L=0$. Thus sequence converges to $0$.

