4. In a vacuum, any body falls freely about $4.9 \mathrm{~m}$ deep in the first second, and in each subsequent second, it falls $9.8 \mathrm{~m}$ more than in the previous one.

(a) How many meters does the body fall freely in a vacuum in the 20th second?

(b) How many meters does this body fall in 20 seconds?
4. From the text of the problem, we read the first term $a_{1}=4.9$ and the difference of the sequence $d=9.8$. Using the formula for the general term of an arithmetic sequence, we calculate the 20th term $a_{20}=a_{1}+19 d=191.1 \mathrm{~m}$. We use the formula for the sum of the first $n$ terms of an arithmetic sequence $S_{20}=\frac{20}{2}\left(2 a_{1}+19 d\right)=$ $1960 \mathrm{~m}$.

![](https://cdn.mathpix.com/cropped/2024_06_07_93a0a0489a8a740fd9e9g-13.jpg?height=317&width=1642&top_left_y=2331&top_left_x=207)