Question

In the sequence 2001, 2002, 2003, ... , each term after the third is found by subtracting the previous term from the sum of the two terms that precede that term. For example, the fourth term is 2001+2002−2003=2000. What is the 2004th term in this sequence?

Answer 1

The answer is 0.

Explanation:

Let's call the answer a.

We want to find a(2004)

That's an even term. We look at the even terms:

2 2002

4 2000

6 1998

8 1996

10 1994

12 1992

We see that the pattern for the even terms is

"if you add n and a(n), the sum is always 2004."

That is n + a(n) = 2004, or,

a(n) = 2004-n when n is even

So when n = 2004, a(2004) = 2004-2004 = 0

Answer: 0