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  1. #1
    Member ~berserk's Avatar
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    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?
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  2. #2
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    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?
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  3. #3
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    any1?
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by ~berserk View Post
    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.
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