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Which of the following sequences has a constant difference of 4 between every pair of consecutive terms?निम्नलिखित में से किस अनुक्रम का प्रत्येक क्रमागत पदों के बीच अंतर सदैव 4 है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(a_n=4n-7\)\(a_n=4n-7\)
For \(a_n=4n-7\), \(a_{n+1}-a_n=[4(n+1)-7]-(4n-7)=4\), so the common difference is constant and it is an AP. The differences in the other options vary with \(n\). Exam tip: in \(pn+q\), the common difference is \(p\).\(a_n=4n-7\) के लिए \(a_{n+1}-a_n=[4(n+1)-7]-(4n-7)=4\), जो स्थिर है; अतः यह AP है। अन्य विकल्पों में अंतर \(n\) के साथ बदलता है। परीक्षा टिप: \(pn+q\) रूप में सार्वांतर \(p\) होता है।
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