Let’s analyze the problem:

The pattern shows a sequence of triangles that increases consistently as the pattern number increases. Here is the information provided:

• Pattern number $n = 1$: 1 triangle.
• Pattern number $n = 2$: 3 triangles.
• Pattern number $n = 3$: 6 triangles.

Step 1: Find the rule

From the sequence of triangles:

1. For $n = 1$, the total number of triangles is $1$.
2. For $n = 2$, the total number of triangles is $3$.
3. For $n = 3$, the total number of triangles is $6$.

This indicates the number of triangles forms the triangular number sequence. The rule for triangular numbers is:

\text{Triangles in nth pattern} = \frac{n \cdot (n+1)}{2}.

Step 2: Simplify the given rule

To match the form shown in the box, the coefficient of $n$ (the value in the box) is the slope of the sequence:

Each time $n$ increases, the number of triangles increases by $n$. The rule becomes:

$\boxed{\frac{n+1}{2}}n.$

Let me know if this explains clearly. Here’s how you help-ful! 🟰1.! What other patt steps