Question

等比数列an,a1=8/9.an=1/3,Sn=65/24,求q,n

Answer 1

a1=a=9/8

an=(9/8)*q^(n-1)=1/3

q^(n-1)=8/27

q^n=(8/27)q

Sn=a(1-q^n)/(1-q)=65/24

(1-q^n)/(1-q)=65/27

[1-(8/27)q]/(1-q)=65/27

27-8q=65-65q

q=2/3

q^(n-1)=8/27

n-1=log(2/3) 8/27

n=3+1=4