`{:("Column A","The nth term of the sequence "a_1","a_2","a_3",….,is definied as "a_(n) = -(a_(n-1))"The first term "a_1 "equals -1", "Column B"),(a_5,,1):}`

Options

A. If column A is larger
B. If column B is larger
C. If the columns are equal
D. If there is not enough information to decide

Answer

To solve the problem, we need to find the value of \( a_5 \) based on the given sequence definition and compare it with the value in Column B, which is 1.

### Step-by-Step Solution:

1. **Understanding the Sequence Definition**:
The sequence is defined such that:
\[ a_n = -a_{n-1} \]
where \( a_1 = -1 \).

2. **Finding the First Few Terms**:
- **For \( n = 1 \)**:
\[ a_1 = -1 \]
- **For \( n = 2 \)**:
\[ a_2 = -a_1 = -(-1) = 1 \]
- **For \( n = 3 \)**:
\[ a_3 = -a_2 = -1 \]
- **For \( n = 4 \)**:
\[ a_4 = -a_3 = -(-1) = 1 \]
- **For \( n = 5 \)**:
\[ a_5 = -a_4 = -1 \]

3. **Summarizing the Values**:
We have calculated the following values:
- \( a_1 = -1 \)
- \( a_2 = 1 \)
- \( a_3 = -1 \)
- \( a_4 = 1 \)
- \( a_5 = -1 \)

4. **Comparison**:
Now we compare \( a_5 \) with the value in Column B:
- Column A: \( a_5 = -1 \)
- Column B: \( 1 \)

5. **Conclusion**:
Since \( -1 < 1 \), we conclude that Column B is larger.

### Final Answer:
Column B is larger than Column A.

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