Question

the triangular arrangement of numbers shown below is known as pascals triangle, credited to french mathematician blaise pascal (1623 - 1662). use inductive reasoning to find the 6 missing numbers. (type whole numbers.)

Explanation:

Step1: Recall Pascal's triangle rule

Each number (except the 1s on the edges) is the sum of the two numbers directly above it.

Step2: Find the first - missing number

The first missing number is above the first 4. Since the numbers above it are 1 and 4, 1 + 4=5.

Step3: Find the second - missing number

The second missing number has 4 and 6 above it. So 4 + 6 = 10.

Step4: Find the third - missing number

The third missing number has 6 and 4 above it. So 6+4 = 10.

Step5: Find the fourth - missing number

The fourth missing number has 4 and 1 above it. So 4 + 1=5.

Step6: Fill in the edge numbers

The edge numbers of Pascal's triangle are always 1. So the first and the last missing numbers are 1.

Answer:

1, 5, 10, 10, 5, 1