数列{an}为等比数列,若a1+a8=387,a4a5=1152,求An

题目

数列{an}为等比数列,若a1+a8=387,a4a5=1152,求An
急………………

答案

a(n)=aq^(n-1),
387=a(1)+a(8)=a+aq^7=a(1+q^7),q^7=387/a-1,
1152=a(4)a(5)=aq^3*aq^4=a^2q^7=a^2[387/a-1]=387a-a^2,
0=a^2-387a+1152=(a-3)(a-384),
a=3,q^7=387/a-1=387/3-1=128,q=2.a(n)=aq^(n-1)=3*2^(n-1),n=1,2,...
或
a=384,q^7=387/a-1=3/384=1/128,q=1/2.a(n)=aq^(n-1)=384/2^(n-1),n=1,2,...