To celebrate SG55 in the Year 2020, an athlete has two proposals for a train programme to complete a 55-km run around Singapore. Proposal (1): To run 800 m on day 1, 960 m on day 2, 1152 m on day 3, and on each successive day, to run a distance that is a constant multiple of the distance run in the previous day. Proposal (2): To run from a starting point O to and from a series of points A, , A2, A3 , .... , increasingly far away in a straight line. The distances between the adjacent points are all 400 m as shown in the figure below. 400 m | 400 m | 400 m | 400 m 1 400 m | 400 m | O A, A2 A3 AA As A6 On day 1, the athlete is to run from O to A, and back to O. On day 2, the athlete is to run from O to A, and back to O, in addition to what he has done on the previous day, i.e. O to A, to O, and then O to A2 to O. This pattern continues for the subsequent days. (i) For Proposal (1), find the least value of n for which the distance run on day n exceeds 55 km. D. = 800 x ()" [4] (ii) For Proposal (2), show that the distance run on day Nis 400N + 400N and hence find the least value of N for which the distance run on day N exceeds 55 km. Determine the distance from O and the direction of travel, of the athlete after he has run exactly 55 km. D, : 800 = 2(400) D2 : 800 + 800 ( 2 ) = 2(400) + 4(400) [5] D3 : 2(400) + 4( 400 ) + 6(400 ) In order to support his training programme, the athlete needs to ensure a sufficient daily calorie intake based on the sum of two components: the athlete's Basal Metabolic Rate (BMR), . the number of calories burnt in a day due to the athlete's running. A person's BMR can be calculated using this equation: BMR = [Ax (Weight in kg)] +[Bx (Height in cm)] +[Cx (Age in years)] + 5 where A, B and C are constants. Based on the above equation, the table below shows the respective biodata and BMR of three persons. Weight (kg) Height (cm) Age (years) BMR Person 1 60 165 25 1511.25 Person 2 78 175 30 1728.75 Person 3 80 178 27 1782.5