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If (a_n=12n+q) and (a_{8n}-a_{3n}=780), what is the value of (n)?यदि (a_n=12n+q) और (a_{8n}-a_{3n}=780) है, तो (n) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 1313
Given \(a_n=12n+q\), we get \(a_{8n}=12(8n)+q=96n+q\) and \(a_{3n}=12(3n)+q=36n+q\). Hence, \(a_{8n}-a_{3n}=(96n+q)-(36n+q)=60n\). Since \(60n=780\), \(n=13\). The constant \(q\) cancels because it occurs in both terms. Exam tip: substitute the required indices into the term formula first, then take their difference.दिया है कि \(a_n=12n+q\)। अतः \(a_{8n}=12(8n)+q=96n+q\) और \(a_{3n}=12(3n)+q=36n+q\)। इसलिए \(a_{8n}-a_{3n}=(96n+q)-(36n+q)=60n\)। अब \(60n=780\), इसलिए \(n=13\)। यहाँ \(q\) दोनों पदों में होने के कारण कट जाता है। परीक्षा टिप: ऐसे प्रश्नों में पहले दिए गए पदों के सूचकांक को सूत्र में रखकर अंतर निकालें।
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