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The first line is 1, the second line is 2, 3, 4, the third line is 5, 6, 7, 8.9, and the fourth line is 10.11.12, 13, 14, 15, 16
The last number in the first line is 1 (1 & # 178;), the last number in the second line is 4 (2 & # 178;), and the last number in the third line is 9 (3 & # 178;)
Therefore, the last number in line n is n & # 178;, and the last number in the previous line is (n-1) &# 178;
Therefore, the total number of numbers in line n is n & # 178; - (n-1) &# 178; = 2N-1
The first number in line n is (n-1) &# + 1
According to the summation formula of arithmetic sequence, the sum is [(n-1) &# 178; + 1 + n & # 178;] × (2n-1) / 2 = (n & # 178; - N + 1) (2n-1) / 2
RELATED INFORMATIONS
- 1. Observe the following table: the first line 1, the second line 1 2 1, the third line 1 2 4 2 1, the fourth line 1 2 4 8 4 2 1 According to the above arrangement rule, the sum of all numbers in the nth row in the sequence table is_________ . First line 1 Second line 1 2 1 The third line 1 2 4 2 1 The fourth line 1 2 4 8 4 2 1
- 2. Arrange the positive integers into the following table according to certain rules: the first line 1, the second line 2 3, the third line 4 5 6, the fourth line 7 8 9 10. What's the 12th in line 2002?
- 3. The first line is 1. The second line is 2, 3 and 4. The third line is 3, 4, 5, 6 and 7. The fourth line is 4, 5, 6, 7, 8, 9 and 10. Q: what's the sum of line 200?
- 4. Divide positive even numbers into arrays: (2), (4,6), (8,10.12), (14.16.18.20) What is the sum of the numbers in group n?
- 5. Observe the numbers - 1, 2, 7, 14, 23, 34 According to this law, the nth number is______ ．
- 6. Observe the numbers - 1, 2, 7, 14, 23, 34 According to this law, the nth number is______ ．
- 7. Fill in the number of safety rules: 1 / 2, 8 / 13, 21 / 34, (), (), ()
- 8. Is the result of 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 +. + 2007 odd or even
- 9. The five numbers are 24:00: 1, 13 7 13 8 29 2, 17 6 30 23 26 3, 14 29 3 6 19 4, 7 19 14 17 21 5, 19 21 23 15 11
- 10. According to the following rule, form a number table with positive integers, then which row and number is 2008 in the table 1；2,3；4,5,6；7,8,9,10；………………
- 11. Natural numbers are arranged in the following table according to certain rules. What is the fifth book on line 60? one 3 5 7 9 11 13 15 17 …… Want to have the train of thought that solves a problem and calculate formula! Had better say of compare easy to understand
- 12. Arrange the natural numbers starting from 1 in the following order one 2 3 4 5 6 7 8 9 10 The first number in line n is The last number of N rows is The sum of the numbers in line n is
- 13. The natural numbers of 1-299 are arranged as follows 1 2 5 10 17 26 37... 4 3 6 11 18 27 38... 9 8 7 12 19 28 39... Which numbers are 5 and 13? Who and whose numbers are 100? What are the rules?
- 14. Natural numbers are arranged as follows: one 2 3 4 5 6 7 8 9 …… …… What is the sum of the four numbers (up, down, left and right) adjacent to 2006?
- 15. Arrange the natural numbers according to the law 1 2 5 10…… 4 3 6 11…… 9 8 7 12…… 16 15 14 13…… …… …… ………… 1. Find the number of the 10th row from the top and the 13th column from the left 2. Which row should the number 127 start from and which column should it start from the left? 3. Which row should the number 2000 be in and which column should it be from the left? 1 2 5 10…… 4 3 6 11…… 9 8 7 12…… 16 15 14 13…… …… …… …………
- 16. Arrange natural numbers according to the following rules. Where is 2009? 1 1 column 2 column 3 column 4 column 1 line 1 2 9 10 2 lines 4 3 8 11 3 lines 5 6 7 12 Four lines 16 15 14 13 5 lines 17 ... There are four options A. Line 17, column 44 B. line 18, column 45 C. line 18, column 46 D. line 19, column 48
- 17. The natural numbers of 1, 2, 3 and 4. N are grouped according to the following rules: the first group: (1) the second group: (2, 3) the third group; (4, 5, 6) the fourth group: (7, 8, 9)
- 18. Arrange a group of numbers regularly: 1, - 2, 3, - 4, 5, - 6, 7, - 8, etc (1) What formula do you think can be used to express each of its terms? (2) What is its 100th number (3) Is 2010 the number of this group? If so, what is the number?
- 19. There is a series of numbers in regular order: - 1,2, - 3,4, - 5,6, - 7,8,... Q: what is the sum of the top 100 items in this series? (to calculate the formula process)
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