AoPS Wiki talk:Problem of the Day/June 15, 2011
AoPSWiki:Problem of the Day/June 15, 2011
We can solve this problem by a bit of trial and error.
We can guess she rode days and we get since the mean is clearly and there are terms.
That's a bit too small.
We can add to and get . That's still too small.
Now, we add to get , which is the total we want.
We started with days and added more, so there are days in total. We can add days to her starting day, Monday, to find her final day. Our answer is thus
On the first day, Jenny rode miles. On the second day, she rode miles. On the third day, she rode miles.
This is the sequence which is an arithmetic sequence: first term , common difference .
We are trying to find the number of terms such that the partial sum of the sequence is .
The formula for the sum of a partial sequence is , where is the first term, is the number of terms, and is the common difference. (Try to derive it!)
Let and Then we have:
The second root is not an integer, so the workout lasted for days. The day after Monday is .