In a sports club (15) members join on the first day and (5) more members join each next day. How many members join in (7) days?
Answer and explanation
Correct answer: 210
The daily number of new members forms an AP: \(15, 20, 25, \ldots\), where \(a=15\), \(d=5\), and \(n=7\). Thus, \(S_7=\frac{7}{2}[2(15)+(7-1)5]=\frac{7}{2}(60)=210\). Therefore, 210 members join in 7 days. The value 195 is the sum for only the first 6 days. Exam tip: When a word problem asks for a total in an AP, use the sum formula \(S_n\), not just the \(n\)th-term formula.
Frequently asked questions
What is the correct answer to this question?
210
Why is this the correct answer?
The daily number of new members forms an AP: \(15, 20, 25, \ldots\), where \(a=15\), \(d=5\), and \(n=7\). Thus, \(S_7=\frac{7}{2}[2(15)+(7-1)5]=\frac{7}{2}(60)=210\). Therefore, 210 members join in 7 days. The value 195 is the sum for only the first 6 days. Exam tip: When a word problem asks for a total in an AP, use the sum formula \(S_n\), 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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