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If (a_n=7n+c) and (a_6=61), what is (r) when (a_{4r}=299)?यदि (a_n=7n+c) और (a_6=61) है, तो (a_{4r}=299) होने पर (r) क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 1010
Given \(a_n=7n+c\). Substituting \(n=6\), \(a_6=42+c=61\), so \(c=19\). Now \(a_{4r}=7(4r)+19=28r+19\). From \(28r+19=299\), we get \(28r=280\), hence \(r=10\). If 9 were used, the term would be 271, not 299. Exam tip: first find the constant \(c\) from the given term, then substitute the required index in the formula.दिया है कि \(a_n=7n+c\)। \(n=6\) रखने पर \(a_6=42+c=61\), अतः \(c=19\)। अब \(a_{4r}=7(4r)+19=28r+19\) होगा। \(28r+19=299\) से \(28r=280\), इसलिए \(r=10\)। विकल्प 9 लेने पर पद 271 आएगा, 299 नहीं। परीक्षा टिप: पहले दिए गए पद से अचर \(c\) ज्ञात करें, फिर मांगे गए सूचकांक को सूत्र में रखें।
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