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What will be the (7)th term in (1,8,27,64,125,\ldots)?क्रम (1,8,27,64,125,\ldots) में (7)वाँ पद क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 343343
This is a sequence of cube numbers: \(1=1^3\), \(8=2^3\), \(27=3^3\), \(64=4^3\), and \(125=5^3\). Hence, the \(n\)th term is \(n^3\). Therefore, the 7th term is \(7^3=343\). Although 216 is also a cube, it is \(6^3\), so it is the 6th term. Exam tip: Express the given terms as powers of natural numbers to identify the pattern quickly.यह घन संख्याओं का क्रम है: \(1=1^3\), \(8=2^3\), \(27=3^3\), \(64=4^3\) और \(125=5^3\)। इसलिए \(n\)वाँ पद \(n^3\) है। अतः 7वाँ पद \(7^3=343\) होगा। \(216=6^3\) है, इसलिए वह 6वाँ पद है। परीक्षा टिप: ऐसे क्रम में प्रत्येक पद को किसी प्राकृतिक संख्या के घन के रूप में लिखकर पैटर्न जाँचें।
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