The first row of a theatre has (40) seats and each next row has (7) more seats. Which row will have (187) seats?
Answer and explanation
Correct answer: 22
The number of seats forms an arithmetic progression with first term \(a=40\) and common difference \(d=7\). The number of seats in the \(n\)th row is \(a_n=40+(n-1)\times 7\). Setting this equal to 187 gives \(40+(n-1)\times 7=187\), so \(7(n-1)=147\), \(n-1=21\), and \(n=22\). Thus, the 22nd row has 187 seats. The 24th row would have \(40+23\times7=201\) seats, so it is not correct. Exam tip: in row-number AP questions, equate the given value to \(a_n=a+(n-1)d\).
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
The number of seats forms an arithmetic progression with first term \(a=40\) and common difference \(d=7\). The number of seats in the \(n\)th row is \(a_n=40+(n-1)\times 7\). Setting this equal to 187 gives \(40+(n-1)\times 7=187\), so \(7(n-1)=147\), \(n-1=21\), and \(n=22\). Thus, the 22nd row has 187 seats. The 24th row would have \(40+23\times7=201\) seats, so it is not correct. Exam tip: in row-number AP questions, equate the given value to \(a_n=a+(n-1)d\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Word problems based on APs.
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