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If the square of its term number is added to each term of (7, 11, 15,\ldots), will the new sequence be an arithmetic progression?यदि (7, 11, 15,\ldots) में हर पद में उसकी पद संख्या का वर्ग जोड़ा जाए, तो क्या नया अनुक्रम अंकगणितीय श्रेणी होगा?
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Correct answer:सही उत्तर: No, because new differences will not be equalनहीं, क्योंकि नए अंतर समान नहीं होंगे
The added squares (1,4,9,\ldots) have differences (3,5,\ldots), which are not equal, so the new sequence will not remain arithmetic. Squares of term numbers do not create equal differences.नए जोड़े गए वर्ग (1,4,9,\ldots) के अंतर (3,5,\ldots) समान नहीं हैं, इसलिए नया अनुक्रम अंकगणितीय नहीं रहेगा। पद संख्या के वर्ग से समान अंतर नहीं बनता।
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