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20 Days to Go(-4 Days) AS&GS

April 14, 2018
Let an be the nth term of a geometric sequence. If a7=32 and a9=8, which of the following must be true?
.font-size-post{ font-size: 18px; line-height: 28px; }
  • a1>0
  • a1-a2>0
  • a2+a3+...+a100>0
.font-size-post{ font-size: 18px; line-height: 28px; }
  • I and II only
  • I and II only
  • I and II only
  • I , II and III
20 Days to Go(-4 Days) AS&GS
.font-size-post{ font-size: 18px; line-height: 28px; }

要留意 r2=1/4
    r =1/2 or -1/2
很多同學忽略了 -1/2 的值，要留意如果題目的條件項是只有單/雙數項，則另一項的正負值是未知。

.font-size-post{ font-size: 18px; line-height: 28px; }

Statement I is true：
因為單數項>0，a1>0

.font-size-post{ font-size: 18px; line-height: 28px; }

Statement II:
a1 x r6 = a7
a1 = 32x64
    = 2048

.font-size-post{ font-size: 18px; line-height: 28px; } a2 = 1024 or -1024
so, a1 - a2>0
Statement II is true
.font-size-post{ font-size: 18px; line-height: 28px; } Statement III:
Case I : r>0
a2= 1024
20 Days to Go(-4 Days) AS&GS
                              >0
.font-size-post{ font-size: 18px; line-height: 28px; } Case II : r<0
a2= -1024
20 Days to Go(-4 Days) AS&GS
                              <0
.font-size-post{ font-size: 18px; line-height: 28px; } Statement II is false
Answer is A

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20 Days to Go(-4 Days) AS&GS

A. AS GS 問題 ，同學應該將問題回到基本，例如

20 Days to Go(-4 Days) AS&GS
B. 今年熱門問題是圖形類的GS問題 如1991年Q12 ,大家不妨多留意
C. 如上面的例子，同學切勿忘記x2 = 4 的答案是有2個的
20 Days to Go(-4 Days) AS&GS

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