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📰 a_n = 2 + (n - 1) \times 3 = 3n - 1
📰 For the 20th term, $a_{20} = 3(20) - 1 = 59$. However, the question asks for the count of terms, not the value. Since the sequence starts at $n = 1$ and ends at $n = 20$, there are $\boxed{20}$ numbers.Question: A square has a perimeter of $ 40 \, \text{cm} $. If each side is increased by $ 2 \, \text{cm} $, by how many square centimeters does the area increase?
📰 Solution: The original side length of the square is $ \frac{40}{4} = 10 \, \text{cm} $. The original area is $ 10^2 = 100 \, \text{cm}^2 $. After increasing each side by $ 2 \, \text{cm} $, the new side length is $ 12 \, \text{cm} $, and the new area is $ 12^2 = 144 \, \text{cm}^2 $. The increase in area is $ 144 - 100 = 44 \, \text{cm}^2 $.
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