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Which statement correctly classifies the sequence whose \(n\)th term is \(a_n=5-3n\)?जिस अनुक्रम का \(n\)वाँ पद \(a_n=5-3n\) है, उसके सही वर्गीकरण वाला कथन कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is a decreasing AP with common difference \(-3\)यह एक घटती हुई AP है जिसका सार्वांतर \(-3\) है
\(a_{n+1}-a_n=[5-3(n+1)]-(5-3n)=-3\), which is constant for every \(n\). Hence it is an AP; the negative difference makes it decreasing. Exam tip: the coefficient of \(n\) gives the common difference.\(a_{n+1}-a_n=[5-3(n+1)]-(5-3n)=-3\), जो हर \(n\) के लिए स्थिर है। अतः यह AP है और ऋणात्मक सार्वांतर के कारण घटती है। परीक्षा टिप: \(n\) का गुणांक सार्वांतर बताता है।
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