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If (a_n=7n-4), what is (k) for (a_{2k}-a_k=84)?यदि (a_n=7n-4) है तो (a_{2k}-a_k=84) के लिए (k) क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 1212
Given a_n = 7n - 4, we get a_{2k} = 7(2k) - 4 = 14k - 4 and a_k = 7k - 4. Hence, a_{2k} - a_k = (14k - 4) - (7k - 4) = 7k. So, 7k = 84 gives k = 12. If k were 11, the difference would be 77, not 84. Exam tip: when the subscript is 2k, substitute the complete expression 2k for n.दिया है a_n = 7n - 4। अतः a_{2k} = 7(2k) - 4 = 14k - 4 तथा a_k = 7k - 4। इसलिए a_{2k} - a_k = (14k - 4) - (7k - 4) = 7k। अब 7k = 84, इसलिए k = 12। विकल्प 11 लेने पर अंतर 77 आएगा, 84 नहीं। परीक्षा टिप: उपसूचक में 2k होने पर n के स्थान पर पूरा 2k रखें।
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