Question

Maria started training for a 21-km run a month prior to a marathon. In order to build stamina, she decided to gradually increase the distance she runs each training day. On the first day, Maria ran a total of 3km. On the second day and third days, she ran 5 and 7 km respectively. For the succeeding five training days, she ran 9, 11, 13, 15, and 17 km. Determine the distance she will have to run the first day of the 5th week of her training.”

Answer 1

Let $a_1=3, a_2=5, a_3=7, a_4=9, a_5=11, a_6=13, a_7=15, a_8=17.$

We have an arithmetic progression where $a_1 = 3$ is the first term, and $d = 2$ is the common difference.

The $n$ -th term is $a_n=a_1+d(n-1).$

Determine the distance she will have to run the first day of the 5-th week of her training

$$a_{17}=a_1+d(17-1)=3+2(16)=35(km)$$

I think this result does not correspond to Maria's tarining for a 21-km. It is more likely that starting from tenth day of training, Maria will run 21 km daily.