已知数列｛an｝a1=1

来源：学生作业帮编辑：搜搜做题作业网作业帮分类：数学作业时间：2024/08/15 06:27:08

已知数列｛an｝a1=1
（1）若a(n+1)=an+n求通项公式an
（2）若a(n+1)=an+2^(n-1)求通项公式an

1)
a1 = 1
a2 = a1 + 1
a3 = a2 + 2
a4 = a3 + 3
……
an = a(n-1) + (n-1)
以上各式子相加,消去等式2端相同的项,最后残留
an = 1 + 1 + 2 + 3 + …… (n-1)
= 1 + [1+(n-1)]*(n-1)/2
= n*(n-1)/2 + 1
2)若a(n+1)=an+2^(n-1)求通项公式an
a1 = 1
a2 = a1 + 2^0
a3 = a2 + 2^1
a4 = a3 + 2^2
……
an= a(n-1) + 2^(n-2)
以上各式子相加,消去等式2端相同的项,最后残留
an = 1 + 2^0 + 2^1 + 2^2 + …… + 2^(n-2)
= 1 + 1*[2^(n-1)-1]/(2-1)
= 2^(n-1)

若数列{An}满足An+1=An^2,则称数列{An}为“平方递推数列”,已知数列{an}中,a1=9,点（an,an+ 已知数列{an}中，a1=56 已知数列{an}满足an+1=an+n,a1等于1,则an=? 已知数列{an}满足an+1=2an+3.5^n,a1=6.求an 已知数列{an}满足a1=1/2,an+1=3an+1,求数列{an}通项公式已知数列{an},a1=1,an+1-an=2^n,求数列{an}通项公式已知数列｛an}中a1=1,an+1-an=3n,求数列｛an}的通项公式. 已知数列{An}满足A1=1,An+1=2An+2^n.求证数列An/2是等差数列已知数列{an},a1=2,an+1=an+2n,则数列的通项公式an=? 已知数列{an},a1=1,an+1=3an/2an+3,(1)求数列{an}的前五项)(2)数列{an}的通项公式已知数列｛an｝满足a1=1,（4^n-1）an=an-1 已知数列{an}满足a1=1，an+1=3an+1．