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What is the (6)th term of (1,8,27,64,\ldots)?क्रम (1,8,27,64,\ldots) का (6)ठा पद क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 216216
The terms are consecutive cube numbers: \(1=1^3\), \(8=2^3\), \(27=3^3\), and \(64=4^3\). Hence, the \(n\)th term is \(n^3\), so the \(6\)th term is \(6^3=216\). \(343\) is a close distractor, but it equals \(7^3\). Exam tip: Write the first few terms as perfect cubes to identify the pattern quickly.क्रम के पद क्रमशः घन संख्याएँ हैं: \(1=1^3\), \(8=2^3\), \(27=3^3\) और \(64=4^3\)। इसलिए इसका \(n\)वाँ पद \(n^3\) है और \(6\)ठा पद \(6^3=216\) होगा। \(343\) निकट का विकल्प है, पर वह \(7^3\) है। परीक्षा टिप: ऐसे क्रम में पहले कुछ पदों को पूर्ण घनों के रूप में लिखकर नियम पहचानें।
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