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If the nth term of a sequence is \(a_n=pn+q\), where \(p\) and \(q\) are constants, which of the following statements is always true?यदि किसी अनुक्रम का nवाँ पद \(a_n=pn+q\) है, जहाँ \(p\) और \(q\) नियतांक हैं, तो निम्नलिखित में से कौन-सा कथन सदैव सत्य है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is an AP with common difference \(p\)यह एक AP है जिसका सार्वांतर \(p\) है
\(a_{n+1}-a_n=[p(n+1)+q]-(pn+q)=p\), which is constant for every \(n\). Hence the sequence is an AP with common difference \(p\), not \(q\). Exam tip: test an AP by subtracting consecutive terms.\(a_{n+1}-a_n=[p(n+1)+q]-(pn+q)=p\) मिलता है, जो हर \(n\) के लिए नियत है। इसलिए अनुक्रम AP है और उसका सार्वांतर \(p\) है, \(q\) नहीं। परीक्षा में क्रमागत पदों का अंतर जाँचें।
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