To determine the missing number in the sequence $5, 11, 29, ?, 245, 731, 2189$, we need to identify the pattern.

First, let's look at the differences between consecutive terms:

• $11 - 5 = 6$
• $29 - 11 = 18$
• $? - 29 = ?$
• $245 - ? = ?$
• $731 - 245 = 486$
• $2189 - 731 = 1458$

Notice that the differences between the terms are increasing. We can see that:

• $6 \times 3 = 18$
• $18 \times 3 = 54$
• $54 \times 3 = 162$
• $162 \times 3 = 486$
• $486 \times 3 = 1458$

This suggests that the sequence increases by multiples of 3.

Thus, the missing differences should be:

• $? - 29 = 54$, which means the missing term is $29 + 54 = 83$.

So, the sequence is:

$5, 11, 29, 83, 245, 731, 2189$

Would you like more details on how this pattern was identified?

Related questions:

1. What is a geometric progression, and how does it differ from this pattern?
2. How can you identify whether a sequence follows an arithmetic or geometric pattern?
3. Can this sequence be expressed as a recursive formula?
4. How do you find missing terms in sequences without a clear multiplication pattern?
5. What are other common types of number sequences?

Tip: When identifying patterns in sequences, look for consistent changes, such as differences or ratios between terms, to reveal hidden rules.