1 2 4 9 23 69 186

Options

A. 2
B. 9
C. 23
D. 69

Explanation

To solve the problem of identifying the wrong number in the series: 1, 2, 4, 9, 23, 69, 186, we will analyze the pattern step by step.

### Step-by-Step Solution:

1. **Identify the Pattern**:
We need to find a consistent pattern in the given series. Let's look at the numbers: 1, 2, 4, 9, 23, 69, 186.

2. **Calculate Differences**:
- From 1 to 2: \(2 - 1 = 1\)
- From 2 to 4: \(4 - 2 = 2\)
- From 4 to 9: \(9 - 4 = 5\)
- From 9 to 23: \(23 - 9 = 14\)
- From 23 to 69: \(69 - 23 = 46\)
- From 69 to 186: \(186 - 69 = 117\)

The differences are: 1, 2, 5, 14, 46, 117.

3. **Look for a Pattern in Differences**:
Let's analyze the differences further:
- From 1 to 2: \(2 - 1 = 1\)
- From 2 to 5: \(5 - 2 = 3\)
- From 5 to 14: \(14 - 5 = 9\)
- From 14 to 46: \(46 - 14 = 32\)
- From 46 to 117: \(117 - 46 = 71\)

The second differences are: 1, 3, 9, 32, 71.

4. **Check for Multiplicative Patterns**:
It appears that each number is derived from the previous number through multiplication and subtraction. Let's analyze this:
- \(1 \times 3 - 1 = 2\)
- \(2 \times 3 - 2 = 4\)
- \(4 \times 3 - 3 = 9\)
- \(9 \times 3 - 4 = 23\)
- \(23 \times 3 - 5 = 64\) (This is where we find an inconsistency)
- \(64 \times 3 - 6 = 186\)

5. **Identify the Wrong Number**:
Following the pattern, the number after 23 should be 64, not 69. Thus, the number 69 is incorrect.

### Conclusion:
The wrong number in the series is **69**. The correct number should be **64**.