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If (a_n=6n+q) and (a_{5n}-a_n=216), what is the value of (n)?यदि (a_n=6n+q) और (a_{5n}-a_n=216) है तो (n) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(9\)\(9\)
Given \(a_n=6n+q\), we get \(a_{5n}=6(5n)+q=30n+q\). Hence, \(a_{5n}-a_n=(30n+q)-(6n+q)=24n\). Now \(24n=216\), so \(n=216/24=9\). Therefore, the correct option is \(9\). The term \(q\) cancels because it occurs in both terms. Exam tip: In such questions, first write \(a_{5n}\) explicitly and then subtract \(a_n\).दिया है \(a_n=6n+q\)। अतः \(a_{5n}=6(5n)+q=30n+q\)। इसलिए \(a_{5n}-a_n=(30n+q)-(6n+q)=24n\)। अब \(24n=216\), इसलिए \(n=216/24=9\)। अतः सही विकल्प \(9\) है। यहाँ \(q\) दोनों पदों में होने के कारण कट जाता है। परीक्षा टिप: ऐसे प्रश्नों में पहले \(a_{5n}\) लिखकर फिर अंतर निकालें।
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