数列【an】满足(n+1)an+1=2(n+2)an+3n2+9n+6,a1=6,求通项公式

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/05/01 14:54:15

(n+1)a(n+1)=2(n+2)an+3n²+9n+6
(n+1)a(n+1)=2(n+2)an+3(n+1)(n+2)
等式两边同除以(n+1)(n+2)
a(n+1)/(n+2)=2an/(n+1) +3
a(n+1)/(n+2) +3=2an/(n+1)+6=2[an/(n+1)+3]
[a(n+1)/(n+2) +3]/[an/(n+1)+3]=2,为定值
a1/(1+1) +3=6/2 +3=6
数列{an/(n+1) +3}是以6为首项,2为公比的等比数列
an/(n+1) +3=6×2^(n-1)=3×2ⁿ
an/(n+1)=3×2ⁿ-3
an=(n+1)(3×2ⁿ-3)=3(n+1)(2ⁿ-1)
n=1时,a1=3×(1+1)(2-1)=6,同样满足通项公式
数列{an}的通项公式为an=3(n+1)(2ⁿ-1)
再问：接上面的第二问bn=3(n+1)/an,{bn}的前n项和Tn

设数列An的前n项满足A1=0,An+1+Sn=n2+2n求通项公式数列{an}对一切自然数n属于N+满足a1+2a2+22a3+...+2n-1an=9-6n,求{an}的通项公式已知数列{an}满足a1=1,an=(an-1)/3an-1+1,(n>=2,n属于N*),求数列{an}的通项公式已知数列{an}的前n项和为Sn,通项an满足Sn+an=1/2(n2+3n-2),求通项公式an. 数列{an}满足a1=1 an+1=2n+1an/an+2n 已知数列{an}满足 a1=3,an+1=an+3n²+3n+2-1\n(n+1),求an的通项公式数列｛an｝满足a1=1,且an=an-1+3n-2,求an 数列{an}中,a1=2,an+1=an+ln(n+1/n),求通项公式已知数列{an}满足,a1=2,a(n+1)=3根号an,求通项an 数列an满足a1+2a2+3a3+...+nan=(n+1)(n+2) 求通项an 设数列an满足a1+3a2+3^2a3+.+3^n-1an=n/3,n∈N*,求数列an的通项公式已知数列an满足a1=1，a（n+3）=3an，数列bn的前n项和Sn=n2+2n+1 ⑴求数列an，bn的通项公式 ⑵