若数列﹛an﹜是公差为d的等差数列,则数列a1+a2,a3+a4,a5+a6·········是公差为多少的等差数列?

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/24 14:54:20

若数列﹛an﹜是公差为d的等差数列,则数列a1+a2,a3+a4,a5+a6·········是公差为多少的等差数列?
由数列﹛an﹜是公差为d的等差数列,有通项为
an=a1+(n-1)d,
从而有 a(2n-1)=a1+[(2n-1)-1]d=a1+(2n-2)d
a2n=a1+(2n-1)d
则数列a1+a2,a3+a4,a5+a6·········即数列{aN},有通项为
aN=a(2n-1)+a2n
=[a1+(2n-2)d]+[a1+(2n-1)d]
=2a1+(4n-3)d
=2a1+d+(4n-4)d
=(2a1+d)+(n-1)4d
说明该数列a1+a2,a3+a4,a5+a6·········即数列{aN},是以
(2a1+d)为首项,
公差是4d的等差数列.
∴数列a1+a2,a3+a4,a5+a6·········即数列{aN},的公差是4d.

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