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What is the next term of (1,8,27,64,125,\ldots)?क्रम (1,8,27,64,125,\ldots) का अगला पद क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 216216
The terms are consecutive cubes of natural numbers: \(1=1^3\), \(8=2^3\), \(27=3^3\), \(64=4^3\), and \(125=5^3\). Therefore, the next term is \(6^3=216\). Note that \(225\) is not a perfect cube. Exam tip: Rewrite sequence terms as \(1^3, 2^3, 3^3\), and so on, to identify the pattern quickly.क्रम के पद क्रमशः प्राकृतिक संख्याओं के घन हैं: \(1=1^3\), \(8=2^3\), \(27=3^3\), \(64=4^3\) और \(125=5^3\)। इसलिए अगला पद \(6^3=216\) होगा। \(225\) एक पूर्ण घन नहीं है। परीक्षा टिप: ऐसे क्रम में पदों को \(1^3, 2^3, 3^3\) आदि के रूप में लिखकर पैटर्न पहचानें।
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