एक ज्यामितीय श्रेणी का तीसरा पद 3 है। इसके पहले पांच पदों का गुणनफल क्या है?

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NDA (Held On: 18 Apr 2021) Maths Previous Year paper
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  1. 81
  2. 243
  3. 729
  4. अपर्याप्त डेटा के कारण निर्धारित नहीं किया जा सकता है

Answer (Detailed Solution Below)

Option 2 : 243
Free
NDA 01/2025: English Subject Test
30 Qs. 120 Marks 30 Mins

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संकल्पना:

आइए अनुक्रम a1, a2, a3 …. an पर विचार करें, जो कि G.P. है

सार्व अनुपात = r = = =

 

गणना​:

विचार करना,

(a = 3) G.P श्रृंखला का तीसरा पद हो

तो, हम पाँच शब्दों को इस प्रकार लिख सकते हैं,

, ,a, ar, ar2

तो, पाँच पदों (P) का गुणनफल होगा,

P = ×  × a × ar × ar= a5

तब से,

a = 3,

∴ पहले पाँच पदों का गुणनफल (P) = 35 = 243

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