Pascal's Triangle is a special pattern of numbers that starts simple and grows in a predictable way. It looks like a pyramid of numbers, and you can build it yourself using just one simple rule.

Everything begins at the top with a single number 1. This starting point is called the apex.

From the apex, every other number in the triangle is found by adding together the two numbers directly above it. That's the only rule you need to remember.

Let's build the first few rows. We start numbering the rows from 0. So, the apex is Row 0.

Row 0 is just: 1

To get the next row, imagine two invisible zeros on either side of the 1 in Row 0. The left '1' in Row 1 comes from $0+1$. The right '1' comes from $1+0$. This is why the outside edges of the triangle are always 1.

Row 1 is: 1 1

Now let's build Row 2 using our rule. The middle number is the sum of the two numbers above it in Row 1, which are $1$ and $1$. So, $1 + 1 = 2$. The outside edges are always 1.

Row 2 is: 1 2 1

See how it works? The '2' is the sum of the '1' and '1' above it. The triangle continues to grow this way, row by row.

Let's keep going to build the first six rows (Rows 0 through 5). We already have the first three.

For Row 3, we look at Row 2 (1 2 1).

• The first number is 1.
• The second number is $1 + 2 = 3$.
• The third number is $2 + 1 = 3$.
• The last number is 1.

So, Row 3 is: 1 3 3 1

For Row 4, we look at Row 3 (1 3 3 1).

• First number: 1
• Second number: $1 + 3 = 4$
• Third number: $3 + 3 = 6$
• Fourth number: $3 + 1 = 4$
• Last number: 1

Row 4 is: 1 4 6 4 1

Now, try to figure out Row 5 on your own before looking at the result below.

Here are the first six rows all together. Notice the perfect symmetry on the left and right sides.

Now that you know the basic rule, you can continue building the triangle as far as you want. Let's check your understanding.

Understanding how to build the triangle is the first step. Every other amazing property of this pattern starts with this simple process of addition.