Find the wrong term in the following number series question.
24,68,120,210,336,504,720

Options

A. 504
B. 210
C. 24
D. 68

Answer

To find the wrong term in the number series: 24, 68, 120, 210, 336, 504, 720, we can follow these steps:

### Step 1: Write down the series
We start by listing the series as given:
- 24, 68, 120, 210, 336, 504, 720

### Step 2: Calculate the first differences
Next, we calculate the differences between consecutive terms:
- Difference between 68 and 24: 68 - 24 = 44
- Difference between 120 and 68: 120 - 68 = 52
- Difference between 210 and 120: 210 - 120 = 90
- Difference between 336 and 210: 336 - 210 = 126
- Difference between 504 and 336: 504 - 336 = 168
- Difference between 720 and 504: 720 - 504 = 216

So, the first differences are:
- 44, 52, 90, 126, 168, 216

### Step 3: Calculate the second differences
Now, we calculate the differences of the first differences:
- Difference between 52 and 44: 52 - 44 = 8
- Difference between 90 and 52: 90 - 52 = 38
- Difference between 126 and 90: 126 - 90 = 36
- Difference between 168 and 126: 168 - 126 = 42
- Difference between 216 and 168: 216 - 168 = 48

So, the second differences are:
- 8, 38, 36, 42, 48

### Step 4: Identify the pattern
The second differences do not show a consistent pattern. Let's analyze the first differences again.

### Step 5: Check for a potential correction
If we replace 68 with 60, we recalculate the first differences:
- Difference between 60 and 24: 60 - 24 = 36
- Difference between 120 and 60: 120 - 60 = 60
- Difference between 210 and 120: 210 - 120 = 90
- Difference between 336 and 210: 336 - 210 = 126
- Difference between 504 and 336: 504 - 336 = 168
- Difference between 720 and 504: 720 - 504 = 216

Now, the new first differences are:
- 36, 60, 90, 126, 168, 216

### Step 6: Calculate the new second differences
Now, we calculate the second differences again:
- Difference between 60 and 36: 60 - 36 = 24
- Difference between 90 and 60: 90 - 60 = 30
- Difference between 126 and 90: 126 - 90 = 36
- Difference between 168 and 126: 168 - 126 = 42
- Difference between 216 and 168: 216 - 168 = 48

The new second differences are:
- 24, 30, 36, 42, 48

### Conclusion
The consistent pattern in the series emerges when we replace 68 with 60. Therefore, the wrong term in the series is **68**.