Find the missing number x, if a certain rule is followed either row wise or column wise. 1) 5, 8, 9 2) 10, 15, 25, 3) 7, 17, x 

To find the missing number \( x \) in the series, we can analyze the numbers given in each row.

1. **Row 1:** \( 5, 8, 9 \)
   - If we look at the differences:
     - \( 8 - 5 = 3 \)
     - \( 9 - 8 = 1 \)
   - The differences do not suggest a clear pattern.

2. **Row 2:** \( 10, 15, 25 \)
   - The differences here are:
     - \( 15 - 10 = 5 \)
     - \( 25 - 15 = 10 \)
   - The difference is increasing by \( 5 \).

3. **Row 3:** \( 7, 17, x \)
   - The difference so far is:
     - \( 17 - 7 = 10 \)

Now, if we observe the rows:
- The first row does not reveal a clear pattern.
- The second row shows a consistent increment (the difference increases by 5).
- The third row starts with a difference of 10.

Let’s see if \( x \) can follow a similar pattern:
- If we assume the difference between \( 17 \) and \( x \) follows the previous row's difference (increasing), we might add \( 15 \) to \( 17 \):
  - \( 17 + 15 = 32 \)

Thus, the missing number \( x \) can be \( 32 \).

### Conclusion:
The missing number \( x \) is \( 32 \).

Would you like more details on how I reached this conclusion, or do you have any questions? Here are some related questions you might consider:

1. How do the differences in each row help in identifying patterns?
2. What other methods can be used to find missing numbers in sequences?
3. Can you provide an example of a similar puzzle?
4. How would the solution change if more numbers were added to each row?
5. What strategies can help with identifying patterns in mathematical sequences?

**Tip:** Always look for patterns in differences, ratios, or sequences when solving for missing numbers.

Find the missing number x, if a certain rule is followed either row wise or column wise. 1) 5, 8, 9 2) 10, 15, 25, 3) 7, 17, x

Solve the problem of finding the missing number 'x' in a pattern sequence puzzle. This question involves recognizing differences in each row, understanding arithmetic sequence patterns, and applying systematic reasoning. Suitable for students in Grades 6-8.

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