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The first row of an auditorium has 24 seats, and each succeeding row has 4 more seats. A student says that the row with 100 seats is the 19th row because they used \(24+4n=100\). After correcting the student's error, which is the correct row?एक सभागार की पहली पंक्ति में 24 सीटें हैं और प्रत्येक अगली पंक्ति में 4 सीटें अधिक हैं। एक छात्र कहता है कि 100 सीटों वाली पंक्ति 19वीं है, क्योंकि उसने \(24+4n=100\) लिया। छात्र की त्रुटि सुधारने पर सही पंक्ति कौन-सी होगी?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 2020
The increase is zero for the first row, so the formula is \(a_n=24+4(n-1)\), not \(24+4n\). From \(24+4(n-1)=100\), we get \(n-1=19\), hence \(n=20\). The 19th row has only 96 seats. In exams, always check the \(n-1\) term.पहली पंक्ति के लिए वृद्धि शून्य होती है, इसलिए सूत्र \(a_n=24+4(n-1)\) होगा, न कि \(24+4n\)। \(24+4(n-1)=100\) से \(n-1=19\), अतः \(n=20\)। 19वीं पंक्ति में 96 सीटें होंगी। परीक्षा में \(n-1\) अवश्य जाँचें।
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