Answer
$10102_{three}$
Work Step by Step
Rightmost column: $1+1=2\times 1=2_{three}$
record the $2$, no carry,
$\left[\begin{array}{lllll}
& & & & \\
& 1 & 0 & 2 & 1_{three}\\
+ & 2 & 0 & 1 & 1_{three}\\
& - & - & - & -\\
& & & & 2_{three}
\end{array}\right.$
Next column:
$1+2=3=1\times 3+0\times 1=10_{three}$
record the $0$, carry the 1.
$\left[\begin{array}{lllll}
& & 1 & & \\
& 1 & 0 & 2 & 1_{three}\\
+ & 2 & 0 & 1 & 1_{three}\\
& - & - & - & -\\
& & & 0 & 2_{three}
\end{array}\right.$
Next column:
$1+0+0=1=1\times 1=1_{three}$
record the $1$, no carry,
$\left[\begin{array}{lllll}
& & 1 & & \\
& 1 & 0 & 2 & 1_{three}\\
+ & 2 & 0 & 1 & 1_{three}\\
& - & - & - & -\\
& & 1 & 0 & 2_{three}
\end{array}\right.$
Next column:
$1+2=3=1\times 3+0\times 1=10_{three}$
record the $10$
result: $10102_{three}$
