已知递增的等比数列{an}满足a2+a3+a4=28,且a3+2是a2,a4的等差中项,若bn=LOG(2an+1)(在log的右下方)...
问题描述:
已知递增的等比数列{an}满足a2+a3+a4=28,且a3+2是a2,a4的等差中项,若bn=LOG(2an+1)(在log的右下方)...
已知递增的等比数列{an}满足a2+a3+a4=28,且a3+2是a2,a4的等差中项,若bn=LOG(2an+1)(在log的右下方).Sn是数列{anbn}的前n项和,求Sn.
答
a2+a3+a4=28,a2+a4=2(a3+2)得a3=8,a2+a4=20a2=a1q,a3=a1q^2 a4=a1q^3 得q=2或1/2递增则q=2 Sn=log2(a2)+log2(a3)+..+log2(a(n+1))=log2(a2a3..a(n+1)) =log2(2^n*2^(n(n+1)/2)) =(n^2+5n+2)/2