Problem:
Let , and for . How many terms in the sequence are even?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The first few terms in the sequence are
Note that every third term is the sum of two odd numbers, so is even for all . Likewise, and will always be odd because each of them is the sum of an even number and an odd number. Because , there are even numbers in the set.
Note: These are the Lucas numbers.
The problems on this page are the property of the MAA's American Mathematics Competitions