Maths_等差級數

2009-04-18 11:02 pm
In a pile(堆) of sticks(棒), there are 32 sticks in the bottom layer(底層), 29 sticks in the second bottom layer, 26 sticks in the thind bottom layer, and so on. There are ten layer in the pile. The uppermost(最上) 6 layers are used to make a fence(籬笆). Find

a) the number of sticks in the pile.

b) the number of sticks used to make the fence

回答 (1)

2009-04-19 3:24 am
✔ 最佳答案
T(1) = 32
T(2) = 29
T(3) = 26.
Since this is an A.S., first term = a = 32
2nd term = a + d = 29, so d = -3.
Now n = 10, so Sum of all sticks = (10)/2[2 x 32 + (10-1) x (-3)]
= 5[64 - 27] = 5 x 37 = 185.
Sum of T(1) to T(4) = (4/2)[2 x 32 + (4 -1) x (-3)] = (4/2)[64 - 9] = 110.
So sticks used for the fence = total sticks - 110 = 185 - 110 = 75.



收錄日期: 2021-04-13 16:34:19
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090418000051KK01115

檢視 Wayback Machine 備份