Question

1.等比数列{an}的前n项和为Sn 若S3+3S2=0,则公比q=?2.已知向量a

Answer 1

1

S3=a1(1-q^3)/(1-q),S2=a1(1-q^2)/(1-q)

故：a1(1-q^3)/(1-q)=-3*a1(1-q^2)/(1-q)

即：1+q+q^2=-3-3q,即：q^2+4q+4=(q+2)^2=0,故：q=-2

2

|2a-b|^2=(2a-b)·(2a-b)=4|a|^2+|b|^2-4a·b=4+|b|^2-4a·b

=4+|b|^2-4|b|cos(π/4)=4+|b|^2-2sqrt(2)|b|=10

故：|b|^2-2sqrt(2)|b|-6=0,故：|b|=(2sqrt(2)±4sqrt(2))/2

即：|b|=3sqrt(2)或-sqrt(2)(不和题意,舍去)

即：|b|=3sqrt(2)