aron is training for a 10km marathon swim in 18 weeks. each week, his training plan includes a long diistance swim. Over the first 6 weeks, Aron swam a total of 18.75 km. Over the first 10 weeks, Aron swam a total of 36.25 km. Each week, Aron increased the distance he swam following an arithmetic sequence until the final week. Answer the following:
a) By what distance did aron increase his total swimming each week?
b) Determine the distance aron swam in the first week of training?
c) Determine how far aron swam over the 18-week training program.
6 years ago
Answered By Sujalakshmy V
Here , Aron's training plan is an arithmetic sequence and that the total distance that he swam for 6 weeks is given as 18.75 km which means S6 is given
S6 = 18.75
also the total distance he swam for 10 weeks is given which means S10 is given
S10 = 36.25
Applying the formula Sn = (n/2)( 2a+(n-1)d) where a is the first term and d is the common difference,
18.75=3(2a+5d).......(1)
36.25=5(2a+9d).......(2)
On solving (1) and (2) we get d=0.25 and a= 2.5 Km
which means
a) The distance that Aron increased his swimming every week is 0.25 Km.
b) The distance Aron swam in the first week of training is 2.5 Km
c) To find how far did he swam over the 18 weeks means we have to find S18
S18 = 9(2*2.5+17*0.25) =83.25 Km