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On a road there is a tree every 46 meters. If the trees are numbered consecutively, what is the number of the tree 5060 meters p
On a road there is a tree every 46 meters. If the trees are numbered consecutively, what is the number of the tree 5060 meters p
admin
2022-10-18
20
问题
On a road there is a tree every 46 meters. If the trees are numbered consecutively, what is the number of the tree 5060 meters past tree number 56?
选项
A、165
B、110
C、152
D、109
E、166
答案
E
解析
公差d=46,5060/46=110,所以应该是第56棵树以后的第110棵,也就是第110+56=166棵树,选择E。
解法1:首先用一种比较笨的方法解题。从题目中可以看出,所有偶数项2,4,6,8,…,2000是一个等差数列,所有奇数项1,3,5,7,…,1999也是一个等差数列,两者公差都为2,所以有:(2+4+6+8+…+2000)-(1+3+5+7+…+1999)
=1000
解法2:所有偶数项2,4,6,8,…,2000是一个等差数列,所有奇数项1,3,5,7,…,1999也是一个等差数列,这两个数列项数都是1000;两者公差相等(都为2)。并且对应项的差都为1,因此1000项就差了1000个1,因此所求差为1000×1=1000。
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