101, 830, 1075, 1154, 1181, 1190, 1193

Options

A. 830
B. 1075
C. 1190
D. 1193

Explanation

To find the wrong number in the sequence 101, 830, 1075, 1154, 1181, 1190, 1193, we will analyze the differences between consecutive terms and look for a pattern.

### Step-by-Step Solution:

1. **Identify the Sequence:**
The given sequence is:
\[ 101, 830, 1075, 1154, 1181, 1190, 1193 \]

2. **Calculate the Differences:**
We will calculate the differences between each consecutive pair of numbers:
- \( 830 - 101 = 729 \)
- \( 1075 - 830 = 245 \)
- \( 1154 - 1075 = 79 \)
- \( 1181 - 1154 = 27 \)
- \( 1190 - 1181 = 9 \)
- \( 1193 - 1190 = 3 \)

So, the differences are:
\[ 729, 245, 79, 27, 9, 3 \]

3. **Analyze the Differences:**
The differences appear to be decreasing, and we can observe:
- \( 729 = 3^6 \)
- \( 245 \) seems out of place.
- \( 79 \) is not a power of 3, but it is close to \( 81 = 3^4 \).
- \( 27 = 3^3 \)
- \( 9 = 3^2 \)
- \( 3 = 3^1 \)

4. **Identify the Pattern:**
The pattern suggests that the differences should follow powers of 3:
- The expected differences should be \( 729, 243, 81, 27, 9, 3 \).

5. **Find the Incorrect Number:**
Since \( 245 \) is not \( 243 \), we will replace \( 245 \) with \( 243 \):
- If we replace \( 245 \) with \( 243 \), then:
\[ 830 + 243 = 1073 \]
- The next difference should be \( 81 \):
\[ 1073 + 81 = 1154 \]
- This confirms that the correct number should be \( 1073 \) instead of \( 1075 \).

6. **Conclusion:**
The incorrect number in the sequence is \( 1075 \).

### Final Answer:
The wrong number in the sequence is **1075**.