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 the given information, answer the following questions, using concept of Arithmetic Progression.
(i) What is the length of the \(3^{\text{th}}\) lane?
\(m\)
(ii) How long is the \(8^{\text{th}}\) lane than that of \(5^{\text{th}}\) lane?
\(m\)
(iii) (a) While practicing for a race, a student took one round each in first \(5\) lanes. Find the total distance covered by the student.
\(m\)
(b) A student took one round each in lane \(4\) to lane \(8\). Find the total distance covered by the student.
\(m\)