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In order to organise, Annual Sports Day, a school prepared an eight lane running track with an integrated football field inside the track area as shown below: The length of innermost lane of the track is 400 m and each subsequent lane is 7.6 m longer than the preceding lane. Based on given information, answer the following questions, using concept of Arithmetic Progression. (i) What is the length of the 6th lane? (ii) How long is the 8th lane than that of 4th lane? (iii) (a) While practicing for a race, a student took one round each in first six lanes. Find the total distance covered by the student. OR (iii) (b) A student took one round each in lane 4 to lane 8. Find the total distance covered by the student.
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Here AP is 400, 407.6, 415.2, ... (i) $a_6 = 400 + 5(7.6) = 438$ m (1 mark). (ii) $a_8 - a_4 = 30.4$ m (1 mark). (iii) $S_6 = \frac{6}{2}(2 \times 400 + 5 \times 7.6) = 2514$ m (1 + 1 marks). OR (iii) Total distance covered = $S_8 - S_3 = \frac{8}{2}(2 \times 400 + 7 \times 7.6) - \frac{3}{2}(2 \times 400 + 2 \times 7.6) = 2190$ m (1 + 1 marks).