A math problem. 1.2.7.14.23.34. How to find the law

A math problem. 1.2.7.14.23.34. How to find the law

The two adjacent numbers are separated: 1 5 7 9 11
Except for 1, the rule behind is: the number behind = the number in front + 2 * the number of positions - 1
There are: 1, 2, 7, 14, 23, 34, 47, 62

Fill in the number according to the rule: 1, 2 / 3, 5 / 8, 13 / 21,

1 2/3 5/8 13/21 34/55 89/144 233/377 ……
law:
The numerator of the following number is the sum of the numerator of the preceding number and the denominator
The denominator of the following number: the denominator of the preceding number plus the numerator of the principal number

Is the sum of 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 odd or even? Why

Even, because the sum of even and odd numbers is even

Is the sum of 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 odd or even

Even number

24 points: (1) 14 29 3 6 19; (2) 13 14 15 16 17; (3) 19 16 13 14 4; (4) 22 30 13 17 19

(29-14)/(6-3)+19=24
15+(17-14)*(16-13)=24
19-13+16/4+14=24
30/(19-17+13)+22=24

Solve 24 points 7,19,14,17,21

(7*17-14)/21+19=24

Arrange the positive integers into the following table: 1; 2,3,4; 5,6,7,8,9; 10,11,12,13,14,15,16. Which line does 2008 appear in

Line 45
Find out the rule first. From the table, we can see that the last number of each row is the square of the number of rows, while 2008 is more than 44 square and less than 45 square, so 2008 is in the 45th row

What is the 10th number of the 10th row in this table? What is the 10th number of the 10th row in this table?
one
2,3,4,5
6.7,8,9,10,11,12
13,14,15,16,17,18,19,20,21,22

The first line: 1 number, mantissa 1;
The second line: 4 numbers, mantissa 1 + 4 = 5;
The third line: 7 numbers, mantissa 5 + 7 = 12;
The fourth line: 10 numbers, mantissa 12 + 10 = 22;
.
Line n: 3n-2 numbers, mantissa 1 + 4 + 7 +. + 3n-2 = n (3n-1) / 2
Line 9 mantissa: 117
Line 10 number 10: 117 + 10 = 127
n(3n-1)/2>=2008>=(n-1)(3n-4)/2
n=37
Line 36: 36 * 3-2 = 106 numbers, mantissa (37-1) (37 * 3-4) / 2 = 1926;
2008-1926=72
So 2008 is number 72 on line 37

What's the fifth number in the tenth line? What's the fifth number in the tenth line?

Is it a number table arranged in this way
one
2 3
4 5 6
7 8 9 10
.
According to the rule of the number table, the last number in line n is: 1 + 2 +... + n = (n * (n + 1)) / 2
So the last number in line 14 is (14 * 15) / 2 = 105
So the fifth number in line 15 is 105 + 5 = 110
From the inequality (n * (n + 1)) / 2 > 200, the minimum integer n = 20 can be obtained,
So 200 is on line 20
The last number in line 19 is 190,
So 200 is the tenth number in line 20
Jiangsu Wu Yunchao answers for reference!

Observe the number table and fill in the number at "
Observe the number table and fill in the number at "
1 4 5 …
2 3 6 … …
9 8 7 … …
10 … … … …
… … … … …

”Fill in 16