Question

等比数列an中a2－a1＝7，an＝112，Sn＝217

Answer 1

a2-a1=a1(q-1)=7
q-1=7/a1 q=(a1+7)/a1
an=a1q^(n-1)=112
q^(n-1)=112/a1
q^n=q^(n-1)×q=(112/a1)×[(a1+7)/a1]=112(a1+7)/a1^2
Sn=a1(q^n -1)/(q-1)=217
a1[112(a1+7)/袜迹a1^2 -1]/(7/a1)=217 整理，得
a1^2-112a1+735=0
(a1-7)(a1-105)=0
a1=7或此塌a1=105
(1)
a1=7时，q=(a1+7)/a1=(7+7)/7=2
an=a1q^(n-1)=7×2^(n-1)=112
2^(n-1)=16
n-1=4
n=5
(2)
a1=105时，q=(a1+7)/a1=(105+7)/105=16/15
an=a1q^(n-1)=105×(16/15)^(n-1)=112
(16/森好圆15)^(n-1)=16/15
n-1=1
n=2