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If (a_n=3n^2+5n), what is (a_{n+1}-a_n)?यदि (a_n=3n^2+5n) है तो (a_{n+1}-a_n) क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(6n+8\)\(6n+8\)
Here, \(a_{n+1}=3(n+1)^2+5(n+1)=3n^2+11n+8\). Therefore, \(a_{n+1}-a_n=(3n^2+11n+8)-(3n^2+5n)=6n+8\). The option \(6n+6\) results from an incorrect calculation of the constant term. Exam tip: Substitute \(n+1\), expand every bracket, and then subtract \(a_n\).\(a_{n+1}=3(n+1)^2+5(n+1)\) होगा। अतः \(a_{n+1}=3n^2+11n+8\), इसलिए \(a_{n+1}-a_n=(3n^2+11n+8)-(3n^2+5n)=6n+8\)। विकल्प \(6n+6\) में स्थिर पद की गणना गलत है। परीक्षा टिप: \(n+1\) रखने के बाद पूरे व्यंजक का विस्तार करके ही घटाएँ।
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