Question

等比数列an中a1+an=30,a2a(n-1)=81且前n项和为Sn=39

Answer 1

a2a(n-1)=81,即

a1an=81

由a1+an=30解得

a1=3,an=27或a1=27,an=3

由等比数列求和公式Sn=[a1(1-q^n)]/(1-q)=(a1-an*q)/(1-q)=39

分别代入a1,an解得q=3或1/3

由an=a1*q^(n-1)

27=3*3^(n-1)解得n=3,

a1=27,an=3时,同样n=3