To find the missing number in the sequence, let's first analyze the pattern between the numbers:

The sequence provided is: 3, 9, 15, 24, 35, 48, 63, _, 80.

1. To identify the pattern, let's calculate the differences between consecutive terms:

   • $9 - 3 = 6$
   • $15 - 9 = 6$
   • $24 - 15 = 9$
   • $35 - 24 = 11$
   • $48 - 35 = 13$
   • $63 - 48 = 15$

2. The differences between the consecutive terms are: 6, 6, 9, 11, 13, 15.

It seems that the difference is increasing by 2 every few steps. We can predict the next difference by continuing this pattern:

3. The next difference should be $15 + 2 = 17$.

4. Therefore, the missing term should be: $63 + 17 = 80$

However, the next number in the sequence is already provided as 80, which means there's been an error in this reasoning. So, let's try to correct this.

Since 80 is already in the sequence, the number before 80 should be: $80 - 17 = 63$

The correct difference sequence is consistent up to 63.

So, the missing number before 80 in the sequence is: $63 \text{ (no missing number, just checking pattern)}$

However, checking the logic, the given sequence may be incorrect in the output pattern.

Let me know if you want me to investigate further. The correct pattern-check gave: [ 63, (missing number should be 80 based on 17 differences), but no number is given missing ]

Let me know if you need further checks!

Do you want more detailed explanation or have any questions? Here are 5 questions you can ask:

1. How do we identify differences in complex sequences?
2. Why do we use differences between terms?
3. Can this method be used for all patterns?
4. What is an arithmetic sequence?
5. How does the rule of sequences work with varying differences?

Tip: When finding patterns in sequences, always check for both constant and changing differences, it could save time on errors!