Predict the numbers in the sixth role.
1.)1
2.)1,1
3.)1,2,1
4.)1,3,3,1
5.)1,4,6,4,1
6.)?
1,10,10,1
Google "Pascal's Triangle"
This is also called "binomial coefficients"
left and right ends of rows are 1
every element is sum of above to left and right
like 3 = 1+2
and 6 = 3+3
so
1 5 10 10 5 1
You forgot the threes Derek.
1,5,10,10,5,1
I mean the fives.
have you seen Pascal's triangle ?
http://ptri1.tripod.com/
To predict the numbers in the sixth row, we can use a pattern called Pascal's Triangle. Pascal's Triangle is a triangular array of numbers in which each number is the sum of the two numbers directly above it.
Let's break down the fifth row and calculate the sixth row step by step:
1.) 1
2.) 1, 1
3.) 1, 2, 1
4.) 1, 3, 3, 1
5.) 1, 4, 6, 4, 1
To get the next row, we add the adjacent elements from the previous row:
1 + 0 = 1 (Adding a 0 to the beginning accounts for the missing left diagonal element)
1 + 1 = 2
2 + 1 = 3
1 + 3 = 4
3 + 3 = 6
3 + 1 = 4
1 + 0 = 1 (Adding a 0 to the end accounts for the missing right diagonal element)
Therefore, the sixth row of Pascal's Triangle is: 1, 5, 10, 10, 5, 1.
So, the numbers in the sixth row are 1, 5, 10, 10, 5, 1.