數學問題 (英文)

(a)
Since the first row has 1 odd number, the second row has 2, the third row has 3 etc.
The last term of each row is given by: 1+2+3+...+n
1+2+3+...+n = n(n+1)/2
Therefore, the last term in the 6th row = 1+2+3+4+5+6 = 21, i.e. the last term in the 6th row is the 21th odd positive integer.
Similarly, the last term in the 7th row = 1+2+3+4+5+6+7 = 28, i.e. the last term in the 6th row is the 28th odd positive integer.
This shows that the 25th odd positive integer is in the 7th row.

(b)
2n-1 represents the nth term of odd positive integer

21(21+1)/2
=231
Therefore, the last term in the 21st row is the 231th term of odd positive integer.
The 19th integer in the 21st row is the 229th odd positive integer.
2(229)-1=457
Therefore, 457 is the 19th odd positive integer in the 21st row.

(c)
1001=2n-1
n=501
1001 is the 501st odd positive integer
The last term of the 32nd row=32(32+1)/2=528
Since the 32nd row has the 497th term to 528th term of odd positive integer, therefore the odd number 1001 is the 5th term in the 32nd row.

（ａ）postive錯左positive
what is the 25th odd positive integer? in which row of the pattern will this integer appear?
什麼是第25個奇數的正整數？ 在樣式的哪列這個整數是否將出現？

The 25th odd positive integer is 49.
yas, 7th sequence appearance.

第25個奇數的正整數是49.
會,第7個數列出現.

(b)expain錯左explain或者explains
what is the 19th integer that appears in the 21st row? explain how you got your answer?
什麼是出現於第21列的第19個整數？
解釋您怎麼得到了您的答復？

455
(自己寫)

(c)expain錯左explain或者explains
determine the row and the position in that row where the number 1001 occurs. explain how you got your answer?
確定列和位置在那列，第1001年發生。 解釋您怎麼得到了您的答復？

看不懂sorry