To solve the problem of filling in the missing term in the series $3, 6, 11, \_\_, 37$, we analyze the differences between consecutive terms.

Step 1: Calculate the differences

• $6 - 3 = 3$
• $11 - 6 = 5$

The differences are increasing by $2$ (from $3$ to $5$). This suggests the next difference will be $7$.

Step 2: Add the next difference

• $11 + 7 = 18$

So, the missing term is 18.

Step 3: Verify the remaining sequence

• Check the next difference: $37 - 18 = 19$, which is consistent since the differences are increasing by $2$.

Final Answer: 18

Let me know if you would like further clarifications! 😊

5 Related Questions:

1. What are arithmetic progressions, and how do they differ from geometric sequences?
2. Can you identify patterns in sequences that are neither arithmetic nor geometric?
3. How can sequences be used in real-world applications?
4. What happens when the differences in a sequence follow non-linear patterns?
5. How do factorials and powers affect number series?

Tip:

When solving number series problems, always start by looking at the differences between terms to identify patterns.