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What is the general term of the sequence (3,6,11,20,\ldots)?अनुक्रम (3,6,11,20,\ldots) का सामान्य पद क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(a_n=2^n+n\)\(a_n=2^n+n\)
Substituting \(n=1,2,3,4\) in \(a_n=2^n+n\) gives \(3,6,11,20\), respectively. Hence, the correct general term is \(a_n=2^n+n\). Although \(a_n=n^2+2\) matches the first three terms, it gives \(18\), not \(20\), when \(n=4\). Exam tip: verify a proposed rule using at least four given terms.\(n=1,2,3,4\) रखने पर \(a_n=2^n+n\) से क्रमशः \(3,6,11,20\) प्राप्त होते हैं। इसलिए सही सामान्य पद \(a_n=2^n+n\) है। \(a_n=n^2+2\) पहले तीन पद देता है, लेकिन \(n=4\) पर \(18\) देता है, \(20\) नहीं। परीक्षा में नियम को कम-से-कम चार दिए गए पदों पर जाँचें।
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