A2. We find that it is an arithmetic sequence with the first term 18 and a common difference of 4, and the sum of the first $n$ terms is 2000. We write its general term as $a_{n}=18+(n-1) 4$ and the formula for the sum of the first $n$ terms of an arithmetic sequence as $S_{n}=\frac{n}{2}\left(a_{1}+a_{n}\right)=2000$. We get an equation of the form $n^{2}+8 n-1000=0$. The solutions to the equation are $n_{1} \doteq 27,87$ and $n_{1} \doteq-35,87$. We determine that only the positive solution is valid, so it would take 28 days to weave a 20 m long rope. The correct answer is $D$.
A2. We wish to knit a $20 \mathrm{~m}$ long scarf. In how many days will we complete it if on the first day we knit $18 \mathrm{~cm}$, and then each subsequent day we knit $4 \mathrm{~cm}$ more than the previous day?
(A) in 27 days
(B) in 18 days
(C) in 36 days
(D) in 28 days
(E) in 497 days