![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Line up some natural numbers starting from 1 into the following shape, then the number 1 from the left of line 10 is______ ．
The number at the end of line 9 is 9 × 9 = 81; the first number from the left of line 10 is 81 + 1 = 82
Arrange some natural numbers starting from 1 into the shape shown in the upper right figure. Then, the second number from the left of line 25 is ()
Arrange some natural numbers starting from 1 into the shape shown in the figure above on the right. Then, the second number from the left of line 25 is (). Help me to go to school tomorrow
Where is the picture?
Mr. Zhao likes to arrange the number from the first line to the tenth line, except the natural number 0. What is the sum of all the numbers?
one
2 3 4
5 6 7 8 9
10 11 12 13 14 15 16
…………
Method 1: the number of numbers in each row is an arithmetic sequence: 1,3,5,..., (2n-1) the 10th row has 2 * 10 = 19 numbers, so there are 1 + 3 + 5 +. + 19 = 100 numbers in 1-10 rows. Because it is a natural sequence starting with 1, the last number in the 10th row is 100, so the sum of numbers in 1-10 rows is 1 + 2 + 3 +. + 100 = 5050 method 2
Let natural numbers be arranged as follows, what is the first number in line 10
1 3 6 10 15 21.
2 5 9 14 20.
4 8 13 19.
7 12 18...
11 17...
sixteen
The answer is 46
Let me give you an easy to understand explanation
The first number in each row from top to bottom is the difference arithmetic sequence, that is, the difference of adjacent numbers in this column is 1, 2, 3, 4, 5
The sum of the above sequence is very simple
The first number in line 10 is: 1 + (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) = 1 + n (n-1) / 2 = 46
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