在等比数列{an}中,公比q=2,且a1a2...a13=2^13,则a2*a5*a8*a11=
1个回答
展开全部
a1a2...a13=a1^13*q^(1+2+...+12)=a1^13*2^78=2^13
a1=(1/2)^5 a13=a1*q^12=(1/2)^5 *2^12=2^7
a1a2...a13=a2/q*a2*a2q *a5/q*a5*a5q *a8/q*a8*a8*q a11/q*a11*a11q *a13
=a2^3 *a5^3 *a8^3 *a11^3 *a13
=(a2*a5*a8*a11)^3 *2^7
=2^13
a2*a5*a8*a11=2^2=4
a1=(1/2)^5 a13=a1*q^12=(1/2)^5 *2^12=2^7
a1a2...a13=a2/q*a2*a2q *a5/q*a5*a5q *a8/q*a8*a8*q a11/q*a11*a11q *a13
=a2^3 *a5^3 *a8^3 *a11^3 *a13
=(a2*a5*a8*a11)^3 *2^7
=2^13
a2*a5*a8*a11=2^2=4
推荐律师服务:
若未解决您的问题,请您详细描述您的问题,通过百度律临进行免费专业咨询