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 the 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 the concept of Arithmetic Progression.
(i) What is the length of the 6th lane? [1 Marks]
(ii) How long is the 8th lane than that of the 4th lane? [1 Marks]
(iii) (a) While practicing for a race, a student took one round each in the first six lanes. Find the total distance covered by the student. [2 Marks]
OR
(b) A student took one round each in lane 4 to lane 8. Find the total distance covered by the student. [2 Marks]
Solution :
Here a=400 m
d=7.6 m(i) What is the length of the 6th lane? Ans : an=a+(n-1)d a6=400+(6-1)7.6 a6=400+5×(7.6)
a6=400+38
a6=438
(ii) How long is the 8th lane than that of the 4th lane? Ans : a8-a4 = a+7d-(a+3d) = a+7d-a-3d = 4d = 4(7.6)
= 30.4 m
(iii) (a) While practicing for a race, a student took one round each in the first six lanes. Find the total distance covered by the student.
Ans : Sn=n/2[2a+(n-1)d]
S6=6/2[2(400)+(6-1)7.6]
S6=3[800+5×7.6]
S6=3[800+38]
S6=3[838]
S6=2514 m
(iv) (b) A student took one round each in lane 4 to lane 8. Find the total distance covered by the student.
Ans :
S8=8/2[2(400)+(8-1)7.6]
S8=4[800+7×7.6]
S8=4[800+53.2]
S8=4[853.2]
S8=3412.8 m
S3=3/2[2(400)+(3-1)7.6]
S3=1.5[800+2×7.6]
S3=1.5[800+15.2]
S3=1.5[815.2]
S3=1222.8 m
S8-S3 =3412.8-1222.8 =2190 m