Q. 3, 3,6, 18,72,?*

A.360

B. 216

C. 288

D. 144

To solve the sequence \( 3, 3, 6, 18, 72, ? \), let's analyze the pattern:

- From \( 3 \) to \( 3 \): No change.
- From \( 3 \) to \( 6 \): The second term is doubled \( 3 \times 2 = 6 \).
- From \( 6 \) to \( 18 \): The third term is multiplied by \( 3 \), i.e., \( 6 \times 3 = 18 \).
- From \( 18 \) to \( 72 \): The fourth term is multiplied by \( 4 \), i.e., \( 18 \times 4 = 72 \).

The pattern seems to involve multiplying by increasing integers: \( 1, 2, 3, 4, \dots \). Following this pattern, the next step would involve multiplying by \( 5 \):

\[
72 \times 5 = 360
\]

Thus, the next term in the sequence is \( 360 \), and the correct answer is:

**A. 360**

Would you like more details on how sequences work?

Here are 5 related questions:
1. What is the general formula for an arithmetic sequence?
2. How do you find the next term in a geometric progression?
3. Can you explain Fibonacci sequences and how they differ from this pattern?
4. What types of sequences are common in number theory?
5. How do sequences and series relate to calculus?

**Tip**: Identifying the pattern type (arithmetic, geometric, or other) is key to solving sequence problems.

Q. 3, 3,6, 18,72,? A.360 B.216 C.288 D.144

Learn how to identify the pattern in the sequence 3, 3, 6, 18, 72 and find the next term using multiplication by increasing integers. This problem covers key concepts in pattern recognition and sequences, ideal for students in Grades 6-8.

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