The formula to calculate the distance he runs in the n-th week
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The formula he runs in n-th week
To calculate the distance he runs in the n-th week, you need to know the distance he runs in the first week (W0) and the rate at which he increases his distance each week (R).
The formula to calculate the distance he runs in the n-th week is:
Dn = W0 + (n-1) * R
Where:
- Dn is the distance he runs in the n-th week
- W0 is the distance he runs in the first week
- R is the rate at which he increases his distance each week
For example, if he runs 5 miles in the first week (W0) and increases his distance by 2 miles each week (R), you can calculate the distance he runs in the 4th week by using the formula:
D4 = 5 + (4-1) * 2
D4 = 5 + 3 * 2
D4 = 5 + 6
D4 = 11
So, he would run 11 miles in the 4th week.
To calculate the distance he runs in the n-th week, we need to know two pieces of information: the distance he runs in the first week and the rate at which his distance increases.
If we assume that the distance he runs in the first week is d1, and the rate at which his distance increases each week is r, then the formula to calculate the distance he runs in the n-th week can be given by:
Distance in n-th week = d1 + (n - 1) * r
Explanation:
The distance in the first week is given by d1. Since the rate at which his distance increases each week is r, the distance in the second week will be d1 + r, the distance in the third week will be d1 + 2r, and so on.
To find the distance in the n-th week, we need to add (n - 1) times the rate (r) to the distance in the first week (d1). This is because in the second week, we add 1 times the rate (r), in the third week we add 2 times the rate, and so on.
Hence, the formula to calculate the distance he runs in the n-th week is given by d1 + (n - 1) * r.