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Which of the following sequences is an arithmetic progression, that is, the difference between each term and its immediately preceding term remains constant?निम्नलिखित में से कौन-सा अनुक्रम समान्तर श्रेणी है, अर्थात जिसमें प्रत्येक पद और उसके ठीक पिछले पद का अंतर स्थिर रहता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(a_n=3n-2\)\(a_n=3n-2\)
In B, \(a_{n+1}-a_n=[3(n+1)-2]-(3n-2)=3\) for every \(n\), so it is an AP. For \(n^2+1\), the difference changes. Exam tip: compare consecutive differences.विकल्प B में \(a_{n+1}-a_n=[3(n+1)-2]-(3n-2)=3\) हर \(n\) पर स्थिर है, अतः यह समान्तर श्रेणी है। \(n^2+1\) का अंतर बदलता है। टिप: दो क्रमागत पदों का अंतर जाँचें।
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