00:01
So for this problem, we know that joe is going to be running one mile day each day in week one.
00:07
And after each individual week, he's going to add one tenth of a mile to the distance that he's running every day.
00:14
And we want to find his total mileage after 25 weeks of this routine.
00:19
So in order to approach this problem, we can think of it by breaking it down into some of our individual weeks.
00:26
So for instance, for week one, we know that he is running a total of seven days in that week.
00:30
And he's running one mile each day.
00:34
For week two, again there are seven days in this week, but this time he's running one mile plus an extra one tenth of a mile every day.
00:42
And it's the same thing for week three.
00:44
And this time he's running one mile plus that one tenth of a mile from week two, plus an extra one tenth of a mile.
00:51
And so when we write it out like this, we can see that each week we are just going to add an extra one tenth.
00:57
So that means that we can write this as a sum...