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10. Nathan decides to exercise each week by jogging. He starts in week 1 by jogging for 20mins. In week 2 he jogs for 30 mins. in week 3 he jogs for 40 mins. and so on. He keeps a record of the total times he spends jogging. After how many weeks is his total 18290mins.
Arithmetic series, a = 20, d = 10, Sn = 18290
Sn = (n/2)[2a + (n - 1)d]
18290 = (n/2)[40 + 10(n - 1)]
18290 = n[20 + 5(n - 1)]
18290 = n[20 + 5n - 5]
18290 = n[5n + 15]
18290 = 5n2 + 15n
0 = 5n2 + 15n - 18290
0 = n2 + 3n - 3658
Solve quadratic and take positive answer for n (the number of weeks)
ok but is there a way to work it up without using arithematic series? Because we havent learned it yet.
He starts at 20 and ends at 18290, an increase of 18270.
He does this at a rate 10 per week and the number of weeks is increase/rate.