### 1.1 Completing the Table
To complete the table, observe the given sequence of numbers of seats in the provided figures (n):
[tex]\[
\begin{tabular}{|l|l|l|l|r|r|r|r|}
\hline Figure (n) & 1 & 2 & 3 & 4 & 5 & 6 & 10 \\
\hline Number of seats & 4 & 6 & 8 & 10 & 12 & 14 & 22 \\
\hline
\end{tabular}
\][/tex]
From the sequence, we can deduce it by adding 2 seats for each subsequent figure:
- Figure 1: 4 seats
- Figure 2: 6 seats
- Figure 3: 8 seats
- Figure 4: 10 seats
- Figure 5: 12 seats
- Figure 6: 14 seats
- Figure 10: 22 seats
### 1.2 General Mathematical Rule
Based on the given sequence, we can find a general rule to determine the number of seats [tex]\(T(n)\)[/tex] in the nth figure.
From the pattern, it is evident that each figure increases its number of seats by 2 compared to the previous one. This can be modeled by the linear equation:
[tex]\[ T(n) = 2n + 2 \][/tex]
Where:
- [tex]\( n \)[/tex] represents the figure number.
- [tex]\( T(n) \)[/tex] represents the total number of seats in that figure.
### 1.3 Real-Life Example of Patterns
#### 1.3.1 Example of an Arithmetic Pattern
Consider the example of the number of students joining a new school each year.
#### 1.3.2 Pattern Description
Suppose a school is experiencing steady growth in enrollment such that each year, 5 more students join the school compared to the previous year.
- Year 1: 100 students
- Year 2: 105 students
- Year 3: 110 students
- Year 4: 115 students
- ...
#### 1.3.3 Type of Pattern
This pattern is arithmetic.
#### 1.3.4 Reason
The pattern is arithmetic because there is a constant difference (in this case, 5 students) between the number of students each year. An arithmetic pattern is characterized by a constant difference between successive terms.
### 3.4 Reasoning for 1.3.3
The reason the pattern of students joining the school is classified as arithmetic is that the number of students increases by a fixed amount (5 students) each year. An arithmetic sequence is defined by the property that the difference between any two consecutive terms is always constant. This fits the given scenario perfectly, as the increment remains the same annually.
