等比数列{an}中,公比q=2,log2a1+log2a2+log2a3+...+log2a10=25,则a1+a2+...+a10=
问题描述：
等比数列{an}中,公比q=2,log2a1+log2a2+log2a3+...+log2a10=25,则a1+a2+...+a10=
答
log2a1+log2a2+log2a3+...+log2a10=25log2(a1*a2*……*a10)=25log2(a1*a1q*a1q²*……*a1*q^9)=25log2(a1^10*q^(1+2+……+9))=25a1^10*q^45=2^25q=2所以a1^10=2^25÷2^45=2^(-20)真数大于0a1>0所以a1=2^(-2)=1/4...