During her first week of biking, Jenny bikes 3km per day. Each week, she bikes 3km farther per day than she did the previous week.
(a) How many weeks does it take Jenny to get up to 15km per day?(b) How far does Jenny bike on her 31st day?
This problem describes an arithmetic sequence. During her 1st week Jenny bikes a1 = 3 km per day. Each week she adds d = 3 km to her distance. During her nth week she bikes
an = 3 + (n – 1)(3)km per day.
(a) This question is asking for the smallest n with an = 15.
15 = 3 + (n – 1)3
12 = (n – 1)3
4 = n – 1
5 = n
During her 5th week of biking, Jenny will go 15 km per day.
(b) This is a slightly sneaky question, since it's phrased in terms of days instead of weeks. Her 31st day will be during her 5th week of biking, so Jenny will go 15 km that day.