In each of the following number series only one Is wrong . Find out the wrong number in the given number series
251 252 254 227 243 118 154

Options

A. 251
B. 252
C. 227
D. 243

Answer

To solve the problem of finding the wrong number in the series 251, 252, 254, 227, 243, 118, 154, we will analyze the series step by step.

### Step 1: Identify the Series
The given series is:
- 251
- 252
- 254
- 227
- 243
- 118
- 154

### Step 2: Find the Differences
Let's calculate the differences between consecutive numbers in the series:
- 252 - 251 = 1
- 254 - 252 = 2
- 227 - 254 = -27
- 243 - 227 = 16
- 118 - 243 = -125
- 154 - 118 = 36

So, the differences are:
1, 2, -27, 16, -125, 36

### Step 3: Analyze the Differences
Now, let's analyze the differences:
- The first two differences (1 and 2) are positive.
- The third difference (-27) is a significant drop.
- The fourth difference (16) is positive.
- The fifth difference (-125) is a large negative number.
- The last difference (36) is positive.

### Step 4: Look for Patterns
We can observe a potential pattern in the differences:
- The first difference (1) can be seen as \(1^2\).
- The second difference (2) can be seen as \(2^2\).
- The third difference (-27) does not fit the pattern.
- The fourth difference (16) can be seen as \(4^2\).
- The fifth difference (-125) can be seen as \(-5^3\).
- The last difference (36) can be seen as \(6^2\).

### Step 5: Identify the Outlier
From the analysis, it seems that the differences should alternate between squares of positive integers and cubes of negative integers. The third difference (-27) is inconsistent with the pattern.

### Step 6: Correct the Series
If we replace the number 252 with a number that fits the pattern, we can try:
- If we take 251 and subtract \(1^3\) (which is 1), we should get 250 instead of 252.

### Conclusion
Thus, the wrong number in the series is **252**. The correct number should be **250**.