等比数列的前n项和_百度文库 若Sn=189,q=2,an=96,求a1和n; 5 (2)若a1+

Question

等比数列的前n项和_百度文库
若Sn=189,q=2,an=96,求a1和n; 5 (2)若a1+a3=10,a4+a6= ,求a4 和S5; 4 (3)若q=2,S4

Answer 1

(1)Sn=A1(1-q^n)/(1-q)
=(a1-a1q^n)/(1-q)
=(a1-an*q)/(1-q)
Sn=189,q=2,an=96
189=(a1-96*2)/(1-2)
a1=3,
an=a1q^(n-1)
96=3*2^(n-1)
32=2^(n-1)
2^5=2^(n-1)
n-1=5
n=6

(2) a1+a3=10, a4+a6=5/4
a1(1+q^2)=10(1) , a4(1+q^2)=5/4(2)
(2)/(1),得
a4/a1=4/5 /10=1/8=q^3,q=1/2
所以，a1(1+(1/2)^2)=10
a1=8