Question

等比数列{an}同时满足下列三个条件① a1+a6=11 ② a3*a4=32/9 ③三个数2/3*a2,a3^2,a4

Answer 1

A1=a,An=aq^(n-1)

A1+A6=11,A3A4=32/9

则a+aq^5=11,aq^2*aq^3=32/9

所以a^2+32/9=11a,解得a=1/3或者a=32/3

因为aq^2*aq^3=32/9,所以q=2或者q=1/2

2/3A2,A3平方,A4+4/9依次成等差数列,所以a=1/3,q=2,

An=2^(n-1)/3