Problem:
On her first day of work, Janabel sold one widget. On day two, she sold three widgets. On day three, she sold five widgets, and on each succeeding day, she sold two more widgets than she had sold on the previous day. How many widgets in total had Janabel sold after working days?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Note that Janabel has sold a total of widget after day, after days and widgets after days. It can be shown that this pattern continues so that after days, Janabel has sold a total of .
The sum of the first odd numbers is needed. The sum of the first and last is , the sum of the second and th is also , and in fact, there are pairs of numbers that each add up to . Thus the required sum is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions