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If (6,18,54,\ldots) is a geometric progression, what is the value of (a_5-a_3)?यदि (6,18,54,\ldots) गुणोत्तर श्रेढ़ी है, तो (a_5-a_3) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 432432
The first term of this GP is 6 and the common ratio is 3. Thus, \(a_3=6\times 3^2=54\) and \(a_5=6\times 3^4=486\). Therefore, \(a_5-a_3=486-54=432\). Option 486 is only the fifth term, not the required difference. Exam tip: use \(a_n=ar^{n-1}\) to find the required terms of a GP.इस गुणोत्तर श्रेणी में प्रथम पद 6 और सार्व अनुपात 3 है। अतः \(a_3=6\times 3^2=54\) तथा \(a_5=6\times 3^4=486\)। इसलिए \(a_5-a_3=486-54=432\)। विकल्प 486 केवल पाँचवाँ पद है, अंतर नहीं। परीक्षा टिप: गुणोत्तर श्रेणी में \(a_n=ar^{n-1}\) का प्रयोग करके आवश्यक पद निकालें।
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