Find the wrong number in following number series.
`5," "9," "25," "59," "125," "225," "369`

Options

A. A)369
B. B)225
C. C)25
D. D)59

Answer

To find the wrong number in the series: 5, 9, 25, 59, 125, 225, 369, we will analyze the pattern of the series step by step.

### Step 1: Identify the pattern
Let's examine the differences between the consecutive terms:

- 2nd term - 1st term: 9 - 5 = 4
- 3rd term - 2nd term: 25 - 9 = 16
- 4th term - 3rd term: 59 - 25 = 34
- 5th term - 4th term: 125 - 59 = 66
- 6th term - 5th term: 225 - 125 = 100
- 7th term - 6th term: 369 - 225 = 144

So, we have the differences: 4, 16, 34, 66, 100, 144.

### Step 2: Analyze the differences
Now, let's look at the differences of the differences:

- 16 - 4 = 12
- 34 - 16 = 18
- 66 - 34 = 32
- 100 - 66 = 34
- 144 - 100 = 44

The second differences are: 12, 18, 32, 34, 44.

### Step 3: Identify the pattern in the second differences
Now, let's analyze the second differences:

- 18 - 12 = 6
- 32 - 18 = 14
- 34 - 32 = 2
- 44 - 34 = 10

The third differences are: 6, 14, 2, 10.

### Step 4: Identify the incorrect term
From the analysis, we can see that the differences are not consistent, especially around the 4th term.

To check the pattern, let's assume that the 4th term should be 61 instead of 59.

- If we replace 59 with 61, we can check the difference:
- New 4th term - 3rd term: 61 - 25 = 36
- New 5th term - new 4th term: 125 - 61 = 64

Now, the differences would be: 4, 16, 36, 64, 100, 144, which are perfect squares (2^2, 4^2, 6^2, 8^2, 10^2, 12^2).

### Conclusion
Thus, the wrong term in the series is **59**, and it should be **61**.