- #1

Vali

- 48

- 0

$$a_{n+1}=\begin{cases}

a_{n}+\frac{1}{2} & \text{ if } n \ is \ even \\

\frac{a_{n}}{3} & \text{ if } n \ is \ odd

\end{cases}$$

I need to find $$\lim_{n\rightarrow \infty }a_{2n+1}$$

I tried something but I didn't get too far.I rewrite the sequence:$a_{1}=1$, $$a_{n+1}=\begin{cases}

a_{n}+r & \text{ if } n \ is \ even \\

q \cdot a_{n} & \text{ if } n \ is \ odd

\end{cases}$$

where $q,r\in (0,1)$ but I don't know how to write $a_{2n+1}$ with $q$ and $r$