14. Case Study-2 A jogger is training for a 5 km charity run. He starts with a run of 400 m; then he increases the distance he runs by 200 m each day 205 top op () O How many days does it take the jogger to reach a distance of 5 km in training? 2.5 day What total distance will he have run in training by then? 2 (ii) 2​

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Q- A jogger is training for a 5 km charity run. He starts with a run of 400 m then he increases the distance he runs by 200 m each day. How many days does it take the jogger to reach a distance of 5 km in training? What total distance will he have run in training by then?

Given,

Total distance = 5km

The distance covered on the first day = 400m

He increases the distance he runs by 200 m each day

To Find,

Days taken to reach a distance of 5km =?

The total distance will he have run in training by then =?

Solution,

The distance covered on the first day = 400m

The distance covered on the second day = 400m + 200 = 600m

The distance covered on the third day = 600m + 200m = 800m

This is an AP as difference between each day is same.

Therefore, a = 400m and common difference = 200m

According to the question, nth term of AP = 5k = 5000m

By the formula of the nth term in AP, we have

[tex]a_n = a + (n-1)d\\5000 = 400 + (n-1)*200\\5000 - 400= (n-1)*200\\4600/200= (n-1)\\23 + 1 = n\\n =24[/tex]

Days taken to reach a distance of 5km = 24 days

The total distance will he have run in training by then =  The sum up to the nth term in the AP

[tex]S_n = (n / 2)(2a + (n-1)d)\\S_n = (24 / 2)(2*400 + (24-1)200)\\S_n = 12*(800 + 23*200)\\S_n = 12*(800 + 4600)\\S_n = 12*5400\\S_n = 64800[/tex]

Hence, the jogger will take 24 days to reach a distance of 5 km in training. He will have run 64800(64.8km) in training by then.

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