John intends to train for a \(21\)-km half marathon and decides to adopt a training programme. The distance he runs each day is reflected in the table below.
Day, \(n\)
1
2
3
4
5
\(n\)
Distance ran by John (in km)
1
1.4
1.8
2.2
Complete the table above.[2]
Tom also intends to train for the \(21\)-km half marathon but decides to adopt a different training programme. The distance he runs each day is reflected in the table below.
Day, \(n\)
1
2
3
4
5
Distance ran by Tom (in km)
0.5
1
2
4
8
Find, showing your working clearly, the distance Tom ran on the \(n\)th day, leaving your answer in terms of \(n\).[2]
Find the value of \(n\) such that the distance ran by Tom on Day \(n\) is at least the distance required to complete the half marathon.[2]
Solution:
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Answer:(a) \(2.6\) km, \((0.4n+0.6)\) km. (b)(i) \(2^{n-2}\) km. (ii) Every integer \(n\ge7\); the least is 7.