Here is a regular array of triangles First line: 1 The second line 1 Third line: 1 2 1 The fourth line: 1 3 3 1 The fifth line: 1 4 6 4 1 The sixth line; 1 5 10 10 5 1 (1) What characteristics do you find when you carefully observe the triangular number matrix? (2) what is the rule of the third number from the left of each row of the number matrix? What is the third number of the third row of the number matrix First line: 1 The second line 1 Third line: 1 2 1 The fourth line: 1 3 3 1 The fifth line: 1 4 6 4 1 The sixth line; 1 5 10 10 5 1

Here is a regular array of triangles First line: 1 The second line 1 Third line: 1 2 1 The fourth line: 1 3 3 1 The fifth line: 1 4 6 4 1 The sixth line; 1 5 10 10 5 1 (1) What characteristics do you find when you carefully observe the triangular number matrix? (2) what is the rule of the third number from the left of each row of the number matrix? What is the third number of the third row of the number matrix First line: 1 The second line 1 Third line: 1 2 1 The fourth line: 1 3 3 1 The fifth line: 1 4 6 4 1 The sixth line; 1 5 10 10 5 1

The number in the next line is the sum of two adjacent numbers in the previous line, such as the fifth line 1 = 0 + 1; 4 = 1 + 3
；6=3+3；4=3+1；1=1+0.

As shown in the figure, the third number from the left in line 102 is ()

Number 3 from left:
Third line 1
The fourth line 1 + 2
The fifth line is 1 + 2 + 3
.
Line 102 1 + 2 +... + 100 = 101 * 100 / 2 = 5050
[questions are welcome]

1, 111, 21, 133, 114, 641. What is the third number from the left of line 1997?
one
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
.
What is the third number from the left of line 1997?

The third number in the second row is 1
The third number in the third row is 1 + 2 = 3
The third number in the fourth row is 1 + 2 + 3 = 6
……
The third number from the left of line 1997
1+2+3+…… +1996=1996（1+1996）/2=1993006

Observe the following two lines of rational numbers: - 2, 4, - 8, 16, - 32, 64 ①-1，2，-4，8，-16，32，… ② (1) what is the order of rational numbers in line 1? (2) What is the relationship between rational number in line 2 and rational number in line 1? (3) Take the seventh number of each row and calculate the sum of the two numbers

(1) The rational numbers in the first line are - 2, (- 2) 2, (- 2) 3, (- 2) 4 (2) the rational number in line 2 is 0.5 times of that in line 1, that is - 2 × 0.5, (- 2) 2 × 0.5, (- 2) 3 × 0.5, (- 2) 4 × 0.5 (3) according to the meaning: (- 2) 7 + (- 2) 7 × 0.5 = - 128-64 = - 192