Question 158954: Write out the first eight rows of Pascal's triangle.What are the next 2 rows?
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! Pascal's triangle rows have 1's on either side.
So the first and last element in each row is 1.
The other values are sums of the previous row values, other than the second row.
For example, let's look at the 6th row in yours,
1 5 10 10 5 1
The 5th row was
1 4 6 4 1
To find the 6th row using the 5th row, first you start with 1,
Next element is the sum of the previous row's first two elements 1+4=5
and on down the line, 4+6=10
next, 6+4=10
next, 4+1=5
and finally end with a 1.
1 5 10 10 5 1
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.
.
So to do the 7th row, first start with 1,
then the sum of the first two elements, 1+5=6,
and on down the line, 5+10=15
next, 10+10=20,
next, 10+5=15,
next, 5+1=6,
and finally a 1.
1 6 15 20 15 6 1
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Next the 8th row, start with 1,
then the sum of the first two elements, 1+6=7,
and on down the line, 6+15=21,
next, 15+20=35,
next, 20+15=35,
next, 15+6=21,
next, 6+1=7,
and finally a 1.
1 7 21 35 35 21 7 1
or altogether
.....................1
...................1 1
.................1 2 1
...............1 3 3 1
.............1 4 6 4 1
.........1 5 10 10 5 1
......1 6 15 20 15 6 1
...1 7 21 35 35 21 7 1
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