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Which of the following sequences has the same difference between consecutive terms throughout?निम्नलिखित में से किस अनुक्रम में क्रमागत पदों का अंतर सदैव समान रहता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(a_n=5n-1\)\(a_n=5n-1\)
For \(a_n=5n-1\), \(a_{n+1}-a_n=[5(n+1)-1]-(5n-1)=5\), a constant difference; hence it is an arithmetic progression. In \(n^2+1\), the differences change. Exam tip: compare consecutive terms’ differences.\(a_n=5n-1\) के लिए \(a_{n+1}-a_n=[5(n+1)-1]-(5n-1)=5\), जो स्थिर है। अतः यह समांतर श्रेणी है। \(n^2+1\) में अंतर बदलता है। परीक्षा में दो क्रमागत पदों का अंतर जाँचें।
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