In a fair, (100) tickets are sold in the first hour and (50) more tickets each next hour. How many tickets are sold in (6) hours?
Answer and explanation
Correct answer: 1350
The hourly ticket sales form an AP with first term \(a=100\), common difference \(d=50\), and \(n=6\) terms. \(S_6=\frac{6}{2}[2(100)+(6-1)50]=3(450)=1350\). Therefore, 1350 tickets are sold in 6 hours. The value 1300 would fail to include the sixth hour’s sale of 350 tickets. Exam tip: When a word problem asks for a total, use \(S_n\), not just the \(n\)th-term formula.
Frequently asked questions
What is the correct answer to this question?
1350
Why is this the correct answer?
The hourly ticket sales form an AP with first term \(a=100\), common difference \(d=50\), and \(n=6\) terms. \(S_6=\frac{6}{2}[2(100)+(6-1)50]=3(450)=1350\). Therefore, 1350 tickets are sold in 6 hours. The value 1300 would fail to include the sixth hour’s sale of 350 tickets. Exam tip: When a word problem asks for a total, use \(S_n\), not just the \(n\)th-term formula.
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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