What is the pattern of the following sequence of numbers, and what are the next 5 numbers in the sequence?
3,6,10,15,21

This sequence is formed by consecutive triangular numbers. Each term is the sum of the natural numbers up to a certain point:

- \( 3 = 1 + 2 \)
- \( 6 = 1 + 2 + 3 \)
- \( 10 = 1 + 2 + 3 + 4 \)
- \( 15 = 1 + 2 + 3 + 4 + 5 \)
- \( 21 = 1 + 2 + 3 + 4 + 5 + 6 \)

The pattern follows this rule: each term adds the next integer to the previous term. For example, to get from 3 to 6, we add 3; from 6 to 10, we add 4; from 10 to 15, we add 5, and so on.

To find the next five numbers:
1. \( 21 + 7 = 28 \)
2. \( 28 + 8 = 36 \)
3. \( 36 + 9 = 45 \)
4. \( 45 + 10 = 55 \)
5. \( 55 + 11 = 66 \)

So, the next five numbers in the sequence are:
**28, 36, 45, 55, 66.**

Would you like a deeper explanation of triangular numbers?

Here are 5 questions to explore this topic further:
1. How can triangular numbers be represented in a geometric form?
2. What is the formula to find the nth triangular number?
3. How does this sequence relate to the concept of arithmetic progression?
4. Can triangular numbers be used in real-life applications? If so, how?
5. Are there any interesting properties of sums involving triangular numbers?

**Tip:** For any sequence, looking at the differences between terms can often reveal the pattern.

What is the pattern of the following sequence of numbers, and what are the next 5 numbers in the sequence? 3,6,10,15,21

Explore the pattern in the sequence 3, 6, 10, 15, 21 by examining triangular numbers. Learn how each term is derived by adding consecutive natural numbers and use this to find the next five numbers: 28, 36, 45, 55, 66. Ideal for students in Grades 6-8.

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