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
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 $D$.