Question 1208236
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Answer: <font color=red>6.92 km</font>


Work Shown


x = amount jogged on day 1 only
x+1.4 = amount jogged on day 2 only
(x+1.4)+1.4 = x+2*1.4 = amount jogged on day 3 only
(x+2*1.4)+1.4 = x+3*1.4 = amount jogged on day 4 only
(x+3*1.4)+1.4 = x+4*1.4 = amount jogged on day 5 only


Add up the expressions mentioned. 
Set the sum equal to 20.6 and solve for x.
day1+day2+day3+day4+day5 = total
x+(x+1.4)+(x+2*1.4)+(x+3*1.4)+(x+4*1.4) = 20.6
(x+x+x+x+x)+(1.4+2*1.4+3*1.4+4*1.4) = 20.6
5x+1.4(1+2+3+4) = 20.6
5x+1.4(10) = 20.6
5x+14 = 20.6
5x = 20.6-14
5x = 6.6
x = 6.6/5
x = 1.32
David jogged 1.32 km on day 1.
He jogged x+4*1.4 = 1.32+4*1.4 = <font color=red>6.92 km</font> on the 5th day.


Check:
day1 = 1.32 km
day2 = 1.32+1.4 = 2.72 km
day3 = 1.32+2*1.4 = 4.12 km  (or 2.72+1.4 = 4.12)
day4 = 1.32+3*1.4 = 5.52 km  (or 4.12+1.4 = 5.52)
day5 = 1.32+4*1.4 = <font color=red>6.92 km</font>  (or 5.52+1.4 = <font color=red>6.92</font>)
total = 1.32+2.72+4.12+5.52+<font color=red>6.92</font> = 20.6
This checksum verifies we have the correct answer.



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Another approach


We have an arithmetic sequence.
The first term is a1 = x.
The common difference is d = 1.4
Sn = sum of the first n terms
Sn = (n/2)*(2*a1+d*(n-1))
Sn = (n/2)*(2x+1.4(n-1))
Then plug n = 5 into this
S5 = (5/2)*(2x+1.4(5-1))


Set this equal to 20.6 and solve for x.
(5/2)*(2x+1.4(5-1)) = 20.6
2.5*(2x+5.6) = 20.6
5x+14 = 20.6
The steps to solving this are shown in the previous section.
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