Find the wrong number in the following number series: `````2,3,7,22,89,440,2677,18740`

Answer

To find the wrong number in the series: 2, 3, 7, 22, 89, 440, 2677, 18740, we will analyze the pattern in the series step by step.

### Step 1: Identify the pattern
The series appears to be generated by a multiplication and addition pattern. Let's denote the numbers in the series as follows:
- a1 = 2
- a2 = 3
- a3 = 7
- a4 = 22
- a5 = 89
- a6 = 440
- a7 = 2677
- a8 = 18740

### Step 2: Check the multiplication and addition
1. From a1 to a2:
- \( a2 = a1 \times 1 + 1 = 2 \times 1 + 1 = 3 \)

2. From a2 to a3:
- \( a3 = a2 \times 2 + 1 = 3 \times 2 + 1 = 6 + 1 = 7 \)

3. From a3 to a4:
- \( a4 = a3 \times 3 + 1 = 7 \times 3 + 1 = 21 + 1 = 22 \)

4. From a4 to a5:
- \( a5 = a4 \times 4 + 1 = 22 \times 4 + 1 = 88 + 1 = 89 \)

5. From a5 to a6:
- \( a6 = a5 \times 5 + 1 = 89 \times 5 + 1 = 445 + 1 = 446 \)

### Step 3: Identify the discrepancy
Now, we notice that:
- The expected value for a6 should be 446, but in the series, we have 440 instead.

### Step 4: Verify the subsequent numbers
Continuing the pattern:
6. From a6 to a7:
- \( a7 = a6 \times 6 + 1 = 446 \times 6 + 1 = 2676 + 1 = 2677 \) (This matches the series)

7. From a7 to a8:
- \( a8 = a7 \times 7 + 1 = 2677 \times 7 + 1 = 18739 + 1 = 18740 \) (This also matches the series)

### Conclusion
The wrong number in the series is **440**, and it should be replaced with **446**.