sequence(20分!!)

Question

5,10,15,20,25,30....
general term:5+5(n-1)
對嗎??
1/1,1/2,1/3,1/4,1/5,1/6......
general term=??
1,1,2,3,5,8,13,21,34,55,89......
general term=??

Answer 1

1.
Your deduction is correct.
But you can further simplifly it as :
5 + 5( n - 1)
= 5 + 5n - 5
= 5n

2.
1 / 1 , 1 / 2 , 1 / 3 , ...
General term = 1 / n

3.
This is 斐波那契數列
It is a very famous sequence in Mathematics.
The general term is

圖片參考：http://upload.wikimedia.org/math/f/c/6/fc603718922bb67e9b0e304080eb937d.png

Quite difficult...
There are also a few more expressions of the general term like these :

圖片參考：http://upload.wikimedia.org/math/9/b/0/9b08722bd58742ce44a6486344176866.png


圖片參考：http://upload.wikimedia.org/math/c/9/3/c9394f393bab2168b0a5fa696783026d.png


圖片參考：http://upload.wikimedia.org/math/5/3/d/53dbfe657cc258b3519951e19dce8fb2.png

Answer 2

5,10,15,20,25,30....中
第n個term 是5的第n個倍數
即是5n
如果你說general term=5+5(n-1)不是不行
5+5(n-1)=5+5n-5=5n
只是5n是最簡單的寫法
寫5+5(n-1)會增加了麻煩

1/1,1/2,1/3,1/4,1/5,1/6......
denominator由1不斷增加
即是第n個term是1/n
其general term為1/n

1,1,2,3,5,8,13,21,34,55,89......
是著名的斐波那契數列(Fibonacci numbers)
有general term
但如何求出,由於太過複雜
請見
http://zh.wikipedia.org/w/index.php?title=%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E6%95%B0%E5%88%97&variant=zh-hk

Answer 3

對 wow