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If a new sequence (4^2,9^2,14^2,\ldots) is formed from (4,9,14,\ldots), is the new sequence an arithmetic progression?यदि (4,9,14,\ldots) से नया अनुक्रम (4^2,9^2,14^2,\ldots) बनाया जाए तो क्या नया अनुक्रम अंकगणितीय श्रेणी है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: No because consecutive differences are not equalनहीं, क्योंकि क्रमागत अंतर समान नहीं हैं
The new terms are (16,81,196), and the differences are (65,115), which are not equal. Squaring generally does not preserve an arithmetic progression.नए पद (16,81,196) हैं और अंतर (65,115) हैं, जो समान नहीं हैं। वर्ग करने से सामान्यतः अंकगणितीय श्रेणी सुरक्षित नहीं रहती।
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