Answer :
To match each sequence with its corresponding pattern, we need to analyze the behavior and structure of each sequence and determine which pattern it follows. Let's break down each sequence and pattern step-by-step.
### Sequence 1: [tex]\(4, 11, 18, 25, \ldots\)[/tex]
- Behavior: Each term increases by 7 from the previous term.
- Pattern: This matches with "Add seven to the previous term."
So, Sequence 1: [tex]\(4, 11, 18, 25, \ldots\)[/tex] corresponds to "Add seven to the previous term."
### Sequence 2: [tex]\(40, 20, 10, 5, \ldots\)[/tex]
- Behavior: Each term is half of the previous term.
- Pattern: This matches with "Divide the previous term by two."
So, Sequence 2: [tex]\(40, 20, 10, 5, \ldots\)[/tex] corresponds to "Divide the previous term by two."
### Sequence 3: [tex]\(100, 96, 92, 88, \ldots\)[/tex]
- Behavior: Each term decreases by 4 from the previous term.
- Pattern: This matches with "Subtract four from the previous term."
So, Sequence 3: [tex]\(100, 96, 92, 88, \ldots\)[/tex] corresponds to "Subtract four from the previous term."
### Sequence 4: [tex]\(4, 12, 36, 108, \ldots\)[/tex]
- Behavior: Each term is three times the previous term.
- Pattern: This matches with "Multiply the previous term by three."
So, Sequence 4: [tex]\(4, 12, 36, 108, \ldots\)[/tex] corresponds to "Multiply the previous term by three."
### Final Matching:
- Sequence 1: [tex]\(4, 11, 18, 25, \ldots\)[/tex] - "Add seven to the previous term."
- Sequence 2: [tex]\(40, 20, 10, 5, \ldots\)[/tex] - "Divide the previous term by two."
- Sequence 3: [tex]\(100, 96, 92, 88, \ldots\)[/tex] - "Subtract four from the previous term."
- Sequence 4: [tex]\(4, 12, 36, 108, \ldots\)[/tex] - "Multiply the previous term by three."
Thus, this is the correct matching:
[tex]\[ \begin{array}{|c|c|} \hline \text{Sequence} & \text{Pattern} \\ \hline 4, 11, 18, 25, \ldots & \text{Add seven to the previous term.} \\ \hline 40, 20, 10, 5, \ldots & \text{Divide the previous term by two.} \\ \hline 100, 96, 92, 88, \ldots & \text{Subtract four from the previous term.} \\ \hline 4, 12, 36, 108, \ldots & \text{Multiply the previous term by three.} \\ \hline \end{array} \][/tex]
### Sequence 1: [tex]\(4, 11, 18, 25, \ldots\)[/tex]
- Behavior: Each term increases by 7 from the previous term.
- Pattern: This matches with "Add seven to the previous term."
So, Sequence 1: [tex]\(4, 11, 18, 25, \ldots\)[/tex] corresponds to "Add seven to the previous term."
### Sequence 2: [tex]\(40, 20, 10, 5, \ldots\)[/tex]
- Behavior: Each term is half of the previous term.
- Pattern: This matches with "Divide the previous term by two."
So, Sequence 2: [tex]\(40, 20, 10, 5, \ldots\)[/tex] corresponds to "Divide the previous term by two."
### Sequence 3: [tex]\(100, 96, 92, 88, \ldots\)[/tex]
- Behavior: Each term decreases by 4 from the previous term.
- Pattern: This matches with "Subtract four from the previous term."
So, Sequence 3: [tex]\(100, 96, 92, 88, \ldots\)[/tex] corresponds to "Subtract four from the previous term."
### Sequence 4: [tex]\(4, 12, 36, 108, \ldots\)[/tex]
- Behavior: Each term is three times the previous term.
- Pattern: This matches with "Multiply the previous term by three."
So, Sequence 4: [tex]\(4, 12, 36, 108, \ldots\)[/tex] corresponds to "Multiply the previous term by three."
### Final Matching:
- Sequence 1: [tex]\(4, 11, 18, 25, \ldots\)[/tex] - "Add seven to the previous term."
- Sequence 2: [tex]\(40, 20, 10, 5, \ldots\)[/tex] - "Divide the previous term by two."
- Sequence 3: [tex]\(100, 96, 92, 88, \ldots\)[/tex] - "Subtract four from the previous term."
- Sequence 4: [tex]\(4, 12, 36, 108, \ldots\)[/tex] - "Multiply the previous term by three."
Thus, this is the correct matching:
[tex]\[ \begin{array}{|c|c|} \hline \text{Sequence} & \text{Pattern} \\ \hline 4, 11, 18, 25, \ldots & \text{Add seven to the previous term.} \\ \hline 40, 20, 10, 5, \ldots & \text{Divide the previous term by two.} \\ \hline 100, 96, 92, 88, \ldots & \text{Subtract four from the previous term.} \\ \hline 4, 12, 36, 108, \ldots & \text{Multiply the previous term by three.} \\ \hline \end{array} \][/tex]
