Question 20

Explanation

To determine the number of visitors on the eighth day, we will analyze the pattern of visitor increases for each library.

Visitor Pattern Analysis for Library A

The visitor data for library $\text{A}$ is: $1205, 1208, 1213, 1220, 1229, 1240, 1253$. Let's calculate the difference between terms:

The addition pattern consists of consecutive odd numbers: $+3, +5, +7, +9, +11, +13$. Thus, the next pattern is $+15$.

The number of visitors to library $\text{A}$ on the eighth day is:

Visitor Pattern Analysis for Library B

The visitor data for library $\text{B}$ is: $210, 212, 216, 222, 230, 240, 252$. Let's calculate the difference between terms:

The addition pattern consists of consecutive even numbers: $+2, +4, +6, +8, +10, +12$. Thus, the next pattern is $+14$.

The number of visitors to library $\text{B}$ on the eighth day is:

Conclusion

Therefore, the number of visitors to library $\text{A}$ and library $\text{B}$ on the eighth day are $1268$ and $266$ people, respectively.