Answer
$a_n=\begin{cases}
n+1,n\in\{1,2,3,4,5,6,7,8,9,10\} \\
\dfrac{3}{n},n>10
\end{cases}$
$b_n=\begin{cases} n-1,n\in\{1,2,3,4,5,6,7,8,9,10\}\\
\dfrac{3}{n},n>10
\end{cases}$
Work Step by Step
Consider the sequences:
$a_n=\begin{cases} n+1,n\in\{1,2,3,4,5,6,7,8,9,10\}\\
\dfrac{3}{n},n>10
\end{cases}$
$b_n=\begin{cases} n-1,n\in\{1,2,3,4,5,6,7,8,9,10\}\\
\dfrac{3}{n},n>10 \end{cases}$
The two sequences have only the first 10 terms different, but have the same limit 0.