已知数列{an}满足an+1=2an+3.5^n,a1=6.求an_数学解答

已知数列{an}满足an+1=2an+3.5^n,a1=6.求an

人气：151 ℃　时间：2020-05-02 13:17:24

解答

a(n+1)-2an=3.5^n,则a2-2a1=3.5^1a3-2a2=3.5^2.a(n+1)-2an=3.5^n以上式子相加,得a(n+1)-a1-Sn=3.5+3.5^2+...+3.5^n=3.5(1-3.5^n)/(1-3.5)=7(3.5^n-1)/5a(n+1)=S(n+1)-Sn--->a(n+1)-S(n+1)=-Sn-Sn-a1=7(3.5^n-1)/5---...