The first and last numbers in each row are always equal to 1 and each number between them is related to the two numbers directly above it.
See solution.
Practice makes perfect
As the name indicates, Pascal's Triangle has a triangular form and it gives us the coefficients of an expanded binomial (a+b)^n. Let's begin by considering n=0.
(a+b)^0 = 1
From the above, we have that the first coefficient in Pascal's Triangle must be 1. Next, let's continue with n=1.
(a+b)^1 = a + bAs we can see, the coefficients of a and b on the right-hand side are 1 and 1. Thus, these are the number in the second row. We will arrange them in such a way that they form a triangle.
To continue writing the triangle we must have in mind the following two facts.
The first and last numbers in each row are always equal to 1.
The middle numbers are found by adding the two numbers directly above it.
By applying the first point mentioned, we can start writing the following row of the triangle as follows.
By using the second point written above, we have that the middle term in the last row is the sum of 1 and 1. Thus, the middle number is 2.
We can continue with this pattern and write the row for which n=3.
By continuing like this, we can write as many rows as we want of Pascal's Triangle.
