The problem in the image is about triangular numbers, which are numbers that can be represented as a triangular pattern of dots. The given sequence is:

$1, 3, 6, 10, \dots$

Formula for Triangular Numbers:

The $n$-th triangular number is given by the formula:

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

Finding the Next Three Numbers:

Let's calculate $T_5$, $T_6$, and $T_7$:

1. $T_5 = \frac{5(5+1)}{2} = \frac{5(6)}{2} = 15$
2. $T_6 = \frac{6(6+1)}{2} = \frac{6(7)}{2} = 21$
3. $T_7 = \frac{7(7+1)}{2} = \frac{7(8)}{2} = 28$

Answer:

The next three triangular numbers are:

$15, 21, 28$

Do you want a further explanation of triangular numbers?

Related Questions:

1. What is the sum of the first 10 triangular numbers?
2. How can you derive the formula for triangular numbers?
3. What is the 100th triangular number?
4. How are triangular numbers related to square numbers?
5. Can you find a real-world application of triangular numbers?

Math Tip:

Triangular numbers appear in many real-life scenarios, such as arranging objects in rows (like bowling pins) or calculating handshake problems in groups!