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?
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![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?](/uploads/image/z/6749120-56-0.jpg?t=%E8%8B%A5%E6%95%B0%E5%88%97%EF%B9%9Ban%EF%B9%9C%E6%98%AF%E5%85%AC%E5%B7%AE%E4%B8%BAd%E7%9A%84%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E5%88%99%E6%95%B0%E5%88%97a1%2Ba2%2Ca3%2Ba4%2Ca5%2Ba6%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%E6%98%AF%E5%85%AC%E5%B7%AE%E4%B8%BA%E5%A4%9A%E5%B0%91%E7%9A%84%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%3F)
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?
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?
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?
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.
应该是4d吧
等差数列有性质:S偶次项-S奇次项=50d 由此得出:a2 a4 a6 …… a100=85 则a1 a2 a3 …… a99 a100=145 应该是偶数(下标)之和减去
a1+a2=a1+a1+d=2a1+d
a3+a4=a1+2d+a1+3d=2a1+5d
a5+a6=a1+4d+a1+5d=2a1+9d
d'=4d
2d