(i) The distance run on the last day is the 21st term of an arithmetic sequence where the first term is 13 km and the common difference is 1.2 km. The formula for the nth term of an arithmetic sequence is:

\(a_n = a + (n-1) imes d\)

Substituting the given values:

\(a_{21} = 13 + 20 imes 1.2 = 37\) km

(ii) The total distance run over 21 days is the sum of the arithmetic sequence. The formula for the sum of the first n terms is:

\(S_n = \frac{n}{2} \times (a + l)\)

where \(l\) is the last term. Substituting the given values:

\(S_{21} = \frac{21}{2} \times (13 + 37) = 525\) km