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If (a_3=45) and (a_7=3645), and (r) is positive, what is (r)?यदि (a_3=45) और (a_7=3645) है, तथा (r) धनात्मक है, तो (r) क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(3\)\(3\)
In a geometric progression, \(a_7=a_3r^{7-3}=a_3r^4\). Thus, \(3645=45r^4\), giving \(r^4=81\). Since \(r\) is positive, \(r=3\). Although \(r=-3\) also satisfies \(r^4=81\), it is excluded by the given positive condition. Exam tip: the exponent of the common ratio equals the difference between the term numbers.ज्यामितीय श्रेणी में \(a_7=a_3r^{7-3}=a_3r^4\)। अतः \(3645=45r^4\), इसलिए \(r^4=81\)। चूँकि \(r\) धनात्मक है, \(r=3\) होगा। \(r=-3\) भी \(r^4=81\) को संतुष्ट करता है, लेकिन धनात्मक होने की शर्त के कारण वह स्वीकार्य नहीं है। परीक्षा टिप: दो पदों के बीच घात हमेशा उनके पदांक का अंतर होती है।
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