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 (type whole numbers.)

Explanation:

Step1: Identify Pascal's triangle rule

Each number is the sum of the two directly above it.

Step2: First and last numbers

The first and last numbers of each row are 1. So the first and last numbers of the new row are 1.

Step3: Second number

Sum of 1 and 4 in the previous row: $1 + 4=5$.

Step4: Third number

Sum of 4 and 6 in the previous row: $4 + 6 = 10$.

Step5: Fourth number

Sum of 6 and 4 in the previous row: $6+4 = 10$.

Step6: Fifth number

Sum of 4 and 1 in the previous row: $4 + 1=5$.

Answer:

1, 5, 10, 10, 5, 1