Question

等比数列{an}中,a1=1,公比为q且|q|≠1,若am=a1a2a3a4a5,则m为

等比数列{an}中,a1=1,公比为q且|q|≠1,若am=a1a2a3a4a5,则m为

Answer 1

∵{an}是等比数列∴an=a1q^(n-1)=q^(n-1)∴am=q^(m-1)=1*q*q^2*q^3*q^4=q^(1+2+3+4)=q^10∵|q|≠1∴m-1=10, m=11

Answer 2

am=a1a2a3a4a5=1*q*q^2*q^3*q^4=q^10
所以m=11

Answer 3

a2=a1q，a3=a1q平方，a4=a1q立方 ，a5=a1q四次方
am=a1a2a3a4a5=a1q十次方，m=10+1=11

Answer 4

am=a1q^(m-1)=q^(m-1)
am=a1a2a3a4a5
=a1*a1q*a1q^2*a1q^3*a1q^4
=(a1)^5q^10
=q^10

∴q^(m-1)=q^10
m-1=10
m=11

Answer 5

an = q^(n-1)
am=a1.a2.a3.a4.a5
= q^(1+2+3+4)
=q^10
m=11