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If \(a_n=kn-8\) and \(a_{19}-a_7=96\), what is \(a_{24}\)?यदि \(a_n=kn-8\) और \(a_{19}-a_7=96\) है तो \(a_{24}\) क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 184184
Given \(a_n=kn-8\), we have \(a_{19}=19k-8\) and \(a_7=7k-8\). Thus, \(a_{19}-a_7=(19k-8)-(7k-8)=12k=96\), so \(k=8\). Now \(a_{24}=24k-8=24\times8-8=184\). Hence, 184 is correct. Exam tip: when subtracting two terms, the constant term \(-8\) cancels out.दिया है \(a_n=kn-8\)। अतः \(a_{19}=19k-8\) और \(a_7=7k-8\)। इसलिए \(a_{19}-a_7=(19k-8)-(7k-8)=12k=96\), जिससे \(k=8\) प्राप्त होता है। अब \(a_{24}=24k-8=24\times8-8=184\)। इसलिए सही उत्तर 184 है। परीक्षा टिप: दो पदों का अंतर लेने पर स्थिर पद \(-8\) कट जाता है।
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