查看完整版本 : 等比數列

momo_1018 2015-9-10 08:31 PM

等比數列

求該數列的通項T(n)及第9項
1. T(2)=1」4,T(7)=8
2. T(5)=7,T(8)=189

top11 2015-9-11 06:48 PM

[quote]原帖由 [i]momo_1018[/i] 於 2015-9-10 08:31 PM 發表 [url=http://www.discuss.com.hk/redirect.php?goto=findpost&pid=425460478&ptid=25082555][img]http://www.discuss.com.hk/images/common/back.gif[/img][/url]
求該數列的通項T(n)及第9項
1. T(2)=1」4,T(7)=8
2. T(5)=7,T(8)=189 [/quote]
1.
[color=#0000ff]T(2) = 1/4 = ar[/color]
[color=#0000ff]T(7) = 8 = ar⁶[/color]

[color=#0000ff](ar⁶)/(ar) = 8/(1/4)[/color]
[color=#0000ff]r⁵ = 32[/color]
[color=#0000ff]r = 2[/color]
[color=#0000ff]a = 1/8[/color]

[color=#0000ff]T(n) = (1/8) × 2ⁿ⁻¹[/color]
[color=#ff0000]T(n) = 2ⁿ⁻⁴[/color]

[color=#ff0000]T(9) = 2⁹⁻⁴ = 2⁵ = 32[/color]
[color=#ff0000][/color]
[color=#ff0000][/color]2.
[color=#0000ff]T(5) = 7 = ar⁴
T(8) = 189 = ar⁷

(ar⁷)/(ar⁴) = 189/7[/color]
[color=#0000ff]r³ = 27[/color]
[color=#0000ff]r = 3[/color]
[color=#0000ff]a = 7/81[/color]
[color=#0000ff][/color]
[color=#0000ff]T(n) = 7/81 × 3ⁿ⁻¹[/color]
[color=#ff0000]T(n) = 7 × 3ⁿ⁻⁵[/color]
[color=#0000ff][/color]
[color=#ff0000]T(9) = 7 × 3⁹⁻⁵ = 7 × 3⁴ = 567[/color]
頁: [1]
查看完整版本: 等比數列