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What is the explicit rule for the sequence (1,4,9,16,\ldots)?अनुक्रम (1,4,9,16,\ldots) का स्पष्ट नियम क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(a_n=n^2\)\(a_n=n^2\)
The terms are \(1^2, 2^2, 3^2, 4^2,\ldots\). Therefore, the \(n\)th term is \(a_n=n^2\). If \(a_n=n^2+1\), the first term would be 2, which does not match the sequence. Exam tip: write the first few terms alongside \(n=1,2,3,\ldots\) to check the pattern.अनुक्रम के पद क्रमशः \(1^2, 2^2, 3^2, 4^2,\ldots\) हैं। इसलिए \(n\)वाँ पद \(a_n=n^2\) होगा। \(a_n=n^2+1\) लेने पर पहला पद 2 आएगा, जो दिए गए अनुक्रम से मेल नहीं खाता। परीक्षा टिप: पहले कुछ पदों को उनके क्रमांक \(n=1,2,3,\ldots\) के साथ लिखकर पैटर्न जाँचें।
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