1. ## statistics

Fiona is training to run a marathon in New York City next year. Each week she increases the distance she runs by 0.5 mile. If she initially started running a 4-mile route, what will be the total number of miles she will run in 52 weeks of training?

this is what i got:

Is it right? We didn't learn how to do this yet so could you show me the process?

2. how about summing up to 52 instead of 51 since you would start running for 4 miles at week 0 and each week increase the distance by 0.5 miles, would this be correct?

can someone help out?

3. any1?

4. Originally Posted by ~berserk
Fiona is training to run a marathon in New York City next year. Each week she increases the distance she runs by 0.5 mile. If she initially started running a 4-mile route, what will be the total number of miles she will run in 52 weeks of training?

this is what i got:

Is it right? We didn't learn how to do this yet so could you show me the process?
Solan, I'm not sure. What I was thinking is that we should rewrite the series so it would start at $i=1$. The upper limit, as a result, would have to be 53. The $i^{th}$ term in the series would then be $3.5+.5i$. So at week 0 $(i=1)$, she runs 4 miles. At week 2 $(i=2)$, she runs 4.5 miles...so on and so forth...

To find out how far she ran in 52 weeks, sum up all the values:

$\sum_{i=1}^{53}3.5+.5i$

Now, Evaluate the sum:

$\sum_{i=1}^{53}3.5+.5i=\sum_{i=1}^{53}3.5+\sum_{i= 1}^{53}.5i=3.5\sum_{i=1}^{53}1+.5\sum_{i=1}^{53}i= 3.5(53)+.5(\frac{(53)(53+1)}{2})=901$.

Thus, she runs a total of 901 miles in 52 weeks.