等差數(shù)列公式

字號(hào):


    等差數(shù)列公式an=a1+(n-1)d
    a1為首項(xiàng),an為第n項(xiàng)的通項(xiàng)公式,d為公差
    前n項(xiàng)和公式為:Sn=na1+n(n-1)d/2
    Sn=(a1+an)n/2
    若m+n=p+q則:存在am+an=ap+aq
    若m+n=2p則:am+an=2ap
    以上n.m.p.q均為正整數(shù)
    文字翻譯
    第n項(xiàng)的值an=首項(xiàng)+(項(xiàng)數(shù)-1)×公差
    前n項(xiàng)的和Sn=首項(xiàng)×n+項(xiàng)數(shù)(項(xiàng)數(shù)-1)公差/2
    公差d=(an-a1)÷(n-1)
    項(xiàng)數(shù)=(末項(xiàng)-首項(xiàng))÷公差+1
    數(shù)列為奇數(shù)項(xiàng)時(shí),前n項(xiàng)的和=中間項(xiàng)×項(xiàng)數(shù)
    數(shù)列為偶數(shù)項(xiàng),求首尾項(xiàng)相加,用它的和除以2
    等差中項(xiàng)公式2an+1=an+an+2其中{an}是等差數(shù)列
    通項(xiàng)公式
    公差×項(xiàng)數(shù)+首項(xiàng)-公差