All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
(a)
Required Distance = \frac{10}{2} [2 \times 8 + (10-1)8] = 440m

(b)
Required Expression = \frac{n}{2} [16+(n-1)8] = 4n(n+1)

To finish at least 5km, we want 4n(n+1) \ge 5000.

Using GC, we solve that the least n = 35

(ii)
Required Expression = \frac{8(2^{n}-1)}{2-1} = 8(2^{n}-1)

Using Graphing Calculator, we find that the least n = 11 for him to have completed exactly 10km. And he would have ran exactly 10km during the 11th stage.

Distance covered in 10th stage = 8(2^{10}-1) = 8184.

Distance away from O = 10000 - 8184 = 1816km.

Thus, when he has run exactly 10km, we know that he is on his 11th stage and is running from O toward A_{11}.

Personal Comments:
Standard APGP question. (ii) gets slightly complicated. Students just need to read really carefully to figure out if the question is look for the single stage distances or total distances. For answers from GC here, they are expected to draw the table to illustrate their findings clearly.

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