急 ! F5 sequence #ex2_1

我去年教過你一次，請看：

http://hk.knowledge.yahoo.com/question/question?qid=7013110300269

Question 3

(a)
Note that [(2n-1)+1]/2 = n is the number of rods from the first longest to the shortest.

Consider an arithmetic sequence with first term being 160 and common difference -4.

T(n) = 32

160 + (n-1)(-4) = 32

160 - 4n + 4 = 32

4n = 132

n = 33

(b)
From the first rod of 160 cm to the 33th rod of 32 cm, the total length is
(160+32)*33/2 = 3168 cm

For the bottom part, there are 2*33-1-33 = 32 rods, starting from 36 cm to 160 cm, the total length is
(36+160)*32/2 = 3136 cm

Therefore, the total length is 6304 cm.