7. A sequence begins $2023,2022,1, \ldots$. After the first two terms, each term is the positive difference between the previous two terms.
What is the value of the $25^{\text {th }}$ term?
A 2010
B 2009
C 2008
D 2007
E 2006
SolUTION
D

The sequence begins
2023, 2022, 1, 2021, 2020, 1, 2019, 2018, 1, . .

From this it seems that, in general, for each non-negative integer $k$, the terms in positions $3 k+1$, $3 k+2$ and $3 k+3$ are $2023-2 k, 2023-2 k-1$ and 1 . [In fact, this holds only provided $2023-2 k-1 \geq 0$, that is, only for $k \leq 1011$. See Problems 7.1 and 7.4.]
Now $25=3 \times 8+1$. Therefore, by putting $k=8$, we deduce that the 25 th term is $2023-2 \times 8=2007$.