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Which of the following sequences has a general term that is a quadratic polynomial (degree 2) in \(n\)?निम्नलिखित में से किस अनुक्रम का सामान्य पद \(n\) का द्विघात बहुपद (घात 2) है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(1,4,9,16,\ldots\)\(1,4,9,16,\ldots\)
For \(1,4,9,16,\ldots\), \(a_n=n^2\), so the rule has degree 2. The first differences are 3, 5, 7, giving a constant second difference of 2. Exam tip: constant second differences indicate a quadratic sequence.क्रम \(1,4,9,16,\ldots\) के लिए \(a_n=n^2\) है, इसलिए इसका नियम द्विघात है। प्रथम अंतर 3, 5, 7 और द्वितीय अंतर 2 है। परीक्षा टिप: स्थिर द्वितीय अंतर द्विघात क्रम पहचानता है।
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