Calculated 25171

Peter trains for a half marathon every day. He ran 1,000m on the first day and increased the training length by 250m daily. On a certain day, Peter ran 21 km in training. That day, he calculated the total distance he had run since the start of training. How many kilometers did Peter run together?

Correct answer:

x =  891 km

Step-by-step explanation:

$$\begin{gathered} a_1=1000\text{m} \\ d=250\text{m} \\ {a}_n=21\text{km}\to \text{m}=21\cdot 1000\text{m}=21000\text{m} \\ {a}_n=a_1+(n-1)\cdot d \\ n=(a_n-a_1)/d+1=(21000-1000)/250+1=81 \\ {x}_1=s_n \\ {x}_1=\frac{a_1+a_n}{2}\cdot n=\frac{1000+21000}{2}\cdot 81=891000\text{m} \\ x=x_1\to \text{km}=x_1:1000\text{km}=891000:1000\text{km}=891\text{km}=891\text{km} \end{gathered}$$

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