25, 49, 121, 289, 529, 1225

Options

A. 121
B. 289
C. 529
D. 1225

Explanation

To solve the problem, we need to analyze the given series: 25, 49, 121, 289, 529, 1225.

### Step 1: Identify the pattern in the series
We start by checking if the numbers are perfect squares.

- 25 = \(5^2\)
- 49 = \(7^2\)
- 121 = \(11^2\)
- 289 = \(17^2\)
- 529 = ?
- 1225 = \(35^2\)

### Step 2: List the square roots of the perfect squares
Next, we list the square roots of the numbers we have identified:

- \(5\), \(7\), \(11\), \(17\), and \(35\)

### Step 3: Check the differences between the square roots
Now, let's examine the differences between these square roots:

- Difference between \(5\) and \(7\) = \(2\)
- Difference between \(7\) and \(11\) = \(4\)
- Difference between \(11\) and \(17\) = \(6\)
- Difference between \(17\) and \(35\) = \(18\)

### Step 4: Identify the missing number
The differences between the square roots do not follow a consistent pattern, but we notice that the square roots are not consecutive integers.

- The square roots of the perfect squares should ideally follow a certain pattern. The missing number should fit in between \(17\) and \(35\).

### Step 5: Check the number 529
Now, we check if \(529\) fits into the pattern. The square root of \(529\) is \(23\) (since \(23^2 = 529\)).

### Step 6: Conclusion
Since \(23\) does not fit into the established pattern of square roots (which should ideally be \(5, 7, 11, 17\) and then a number greater than \(17\) but less than \(35\)), we conclude that \(529\) is the incorrect number in the series.

Thus, the answer is that \(529\) is the wrong number in the series.