Math pattern...help?

Question

The array shows the first four rows of the triangle attributed to the French mathematician Blaise Pascal. Study the triangle and determine the entries in the tenth row.
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
"Algebra Problems One Step Beyond" by Reuben Schadler

Answer 1

1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 22 35 35 22 7 1
1 8 29 57 70 57 29 8 1

Answer 2

1
1 1
1 2 1
Every number is the addition of the number directly above it plus the number directly above and left of it. It always starts with 1 and you add 1 at the end

1 X1 X2 X3 1
1 X1+1 X2+X1 X3+X2 1+X3 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
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
1 10 45 120 210 252 210 120 45 10

Answer 3

The pattern is (always keep the ones):
top row - 1,
second row- 1 1
third row - 1 2 1, because you add the two ones from row above it,
fourth row - 1 3 3 1 because 1 + 2 = 3, and, again, 1 + 2 = 3,
fifth row - 1 4 6 4 1, because 1+3=4, 3+3=6, and 1+3=4,
sixth - 1 5 10 10 5 1, because 1+4=5, 4+6=10, 6+4=10, and 4+1=5,
seventh - 1 6 15 20 15 6 1, because 1+5=6, 5+10=15, 10+10=20, 10+5=15, and 5+1=6,
and just to make sure you get it, the eighth is - 1 7 21 35 35 21 7 1, because 1+6=7, 6+15=21, 15+20=35, 20+15=35, 15+6=21, and 6+1=7.

Hope that helps, it's kind of confusing =]

Answer 4

1 0
1 1 0
1 2 1 0
1 3 3 1 0
1 4 6 4 1 0 0
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
....................
anyway, the second number of the next row is equal to the 1st number + the 2nd number of previous row, etc.....
hope this helps

Answer 5

Just multiply each row by 11 to get the next row. 1=11^0 The tenth row would be 11^9

Answer 6

You can see that each number is got by adding the number above it and the number to the left of that number.

Answer 7

Up to line 16 on
http://en.wikipedia.org/wiki/Pascal_triangle

Answer 8

15101051