In the following number series only one number is wrong . Find out the wrong number.
`2" "9" "32" "105" "436" "2195" "13182`

Options

A. 436
B. 2195
C. 9
D. 32

Answer

To find the wrong number in the series `2, 9, 32, 105, 436, 2195, 13182`, we will analyze the pattern in the series step by step.

### Step-by-Step Solution:

1. **Identify the Series**: The given series is `2, 9, 32, 105, 436, 2195, 13182`.

2. **Calculate Differences**: Let's calculate the differences between consecutive terms:
- Difference between 9 and 2: \(9 - 2 = 7\)
- Difference between 32 and 9: \(32 - 9 = 23\)
- Difference between 105 and 32: \(105 - 32 = 73\)
- Difference between 436 and 105: \(436 - 105 = 331\)
- Difference between 2195 and 436: \(2195 - 436 = 1759\)
- Difference between 13182 and 2195: \(13182 - 2195 = 10987\)

So, the differences are: `7, 23, 73, 331, 1759, 10987`.

3. **Look for Patterns**: The differences do not seem to follow a simple arithmetic progression. Let's look for a multiplicative or additive pattern:
- If we analyze the first few terms, we can see:
- From 2 to 9: \(2 \times 4 + 1 = 9\)
- From 9 to 32: \(9 \times 3 + 5 = 32\)
- From 32 to 105: \(32 \times 3 + 9 = 105\)

4. **Check for Consistency**: Continuing this pattern:
- From 105 to 436: \(105 \times 4 + 16 = 436\)
- From 436 to 2195: \(436 \times 5 + 35 = 2195\)
- From 2195 to 13182: \(2195 \times 6 + 42 = 13182\)

5. **Identify the Anomaly**: The pattern seems to hold for all terms except for the transition from 9 to 32. Instead of \(9 \times 3 + 5\) yielding 32, it should yield 30. Thus, the term 32 is incorrect.

6. **Conclusion**: The wrong number in the series is **32**. The correct term should be **30**.