Recurring Mean

Stage: 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

The mean is $(1.\dot{2}+2.\dot{1})/2=3.\dot{3}/2=1.\dot{6}$.

Alternatively, you can convert into fractions, to get the answer of $1\frac{2}{3}$, which is the same as $1.\dot{6}$.

This problem is taken from the UKMT Mathematical Challenges.