This sequence represents the triangular numbers, where each term is the sum of the first $n$ natural numbers. The formula for the $n$-th triangular number is:

$T_n = \frac{n(n+1)}{2}$

The sequence is: 1 ($T_1$), 3 ($T_2$), 6 ($T_3$), 10 ($T_4$), 15 ($T_5$), 21 ($T_6$)...

To find the next number, calculate $T_7$:

$T_7 = \frac{7(7+1)}{2} = \frac{7 \cdot 8}{2} = 28$

Thus, the next number is 28.

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Would you like a deeper explanation or more examples of triangular numbers? Here are 5 related questions:

1. What are the first 10 triangular numbers?
2. How do triangular numbers relate to geometry or visual representations?
3. Can triangular numbers be generalized to other shapes, like squares or pentagons?
4. What is the relationship between triangular numbers and arithmetic progressions?
5. How can triangular numbers be used in real-life applications or problem-solving?

Tip: Triangular numbers are closely linked to the formula for summing consecutive integers!