To determine the pattern rule, let’s examine the changes between each term:

1. Starting Sequence: $100, 330, 1020, 3090$

2. Calculate Ratios:

   • $330 \div 100 = 3.3$
   • $1020 \div 330 = 3.1$
   • $3090 \div 1020 = 3.03$

It appears that each term increases by a multiplying factor that gradually approaches 3. We can approximate this sequence as following a multiplication rule where each term is about 3 times the previous one, with slight variations.

General Rule:

If we approximate with a common ratio of 3, we can write: $a_n = 100 \times 3^{(n-1)}$ for term $n$.

This is an exponential growth pattern where each term roughly triples from the previous term, though with slight deviations.

Would you like to dive into details on approximations in sequences, or perhaps try calculating additional terms? Here are some related questions that could be of interest:

1. How can we determine a precise pattern when ratios aren't exact?
2. What are common types of growth patterns in sequences?
3. How does exponential growth differ from other sequence patterns?
4. What methods exist for verifying patterns in more complex sequences?
5. How can approximation be helpful in identifying patterns?

Tip: In sequences, testing differences or ratios between terms often reveals the underlying rule quickly.