设数列{an}的前n项和为sn,满足2sn=a(n+1)-2^(n+1)+1,n属于n*.且a1,a2+5,a3成等差数列.

题目

设数列{an}的前n项和为sn,满足2sn=a(n+1)-2^(n+1)+1,n属于n*.且a1,a2+5,a3成等差数列.
1 求a1 （答案1）2.bn=an+2^n 求证bn是等比数列 3.求满足an＞4/5 X 3^的最小正整数n
第三小题求解 an=3^n-2^n
an＞4/5 X 3^n

答案

1.2Sn=a(n+1)-2^(n+1) +12S1=2a1=a2 -2²+1=a2-3a2=2a1 +32S2=2a1+2a2=2a1+2(2a1+3)=6a1+6=a3-2³+1=a3-7a3=6a1+13a1、a2+5、a3成等差数列,则2(a2+5)=a1+a32(2a1+3+5)=a1+6a1+133a1=3a1=12.2Sn=a(n+1)-2^(n+...