已知数列{an}满足an+1=2an+3.5^n,a1=6.求an

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/14 15:05:05
已知数列{an}满足an+1=2an+3.5^n,a1=6.求an
xMN0.GvHs,"X,R!eQ6P$?4jibc0Xy34VoL>|+^L?^_PI)Oֶ/M.έ +0@j X.f|cpR]趫'mB5s(l1شDWeq"~H;6z6Ѓ$DhqXjy?\o`ʡY =Sl-vR!ՋF,FYr_S}Vݡ$ jRJD~

已知数列{an}满足an+1=2an+3.5^n,a1=6.求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an+1=2an+3.5^n,a1=6.求an
a(n+1)-2an=3.5^n,则
a2-2a1=3.5^1
a3-2a2=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)/5
a(n+1)=S(n+1)-Sn--->a(n+1)-S(n+1)=-Sn
-Sn-a1=7(3.5^n-1)/5--->Sn=-a1-7(3.5^n-1)/5=-6-7(3.5^n-1)/5
an=Sn-S(n-1)=[-6-7(3.5^n-1)/5]-[-6-7(3.5^(n-1)-1)/5]
=[7*3.5^(n-1)-7*3.5^n]/5
=-3.5^n
有点怪异!

3分之14乘2的n-2次方乘(1.75的n减1次方-1)