To arrange the sequences in ascending order and fill in the blanks, you need to find a pattern in the given numbers and then identify the missing number that fits the sequence. Here’s how to solve each sequence step by step:

Sequence 1: 128, 135, ___

1. Identify the pattern: The sequence is increasing by adding a certain value.
2. Calculate the difference:
   • $135 - 128 = 7$
   • The difference between the first and second number is 7.
3. Add the difference to the last known number:
   • $135 + 7 = 142$
4. Conclusion: The missing number is 142.

Sequence 2: 781, 824, ___

1. Identify the pattern: The sequence is increasing by a certain value.
2. Calculate the difference:
   • $824 - 781 = 43$
   • The difference between the first and second number is 43.
3. Add the difference to the last known number:
   • $824 + 43 = 867$
4. Conclusion: The missing number is 867.

Sequence 3: 389, 427, ___

1. Identify the pattern: The sequence is increasing by a certain value.
2. Calculate the difference:
   • $427 - 389 = 38$
   • The difference between the first and second number is 38.
3. Add the difference to the last known number:
   • $427 + 38 = 465$
4. Conclusion: The missing number is 465.

Final Sequences with Blanks Filled:

• 128, 135, 142
• 781, 824, 867
• 389, 427, 465

Steps Recap:

1. Identify the pattern by finding the difference between consecutive numbers.
2. Apply this difference to the last known number in the sequence.
3. Fill in the missing number using the pattern identified.

Would you like more details on this process or have any questions?

Relative Questions:

1. What is the next number after 142 in the first sequence if the pattern continues?
2. How would you approach a sequence with a decreasing pattern?
3. What if the sequence pattern involves multiplication instead of addition?
4. Can there be more than one correct answer in some sequences?
5. What is the importance of identifying patterns in sequences?
6. How would the solution change if the sequence involved a different arithmetic operation?
7. How do you solve sequences involving geometric progressions?
8. What if the sequence has alternating patterns (e.g., +7, -7)?

Tip:

When identifying patterns in sequences, always check the consistency of the difference or ratio between terms to ensure accuracy.