In a hospital (18) patients come on the first day and (2) more patients come each next day. How many patients come in (9) days?
Answer and explanation
Correct answer: 234
The daily number of patients forms an arithmetic progression: \(18, 20, 22, \ldots\). Here, \(a=18\), \(d=2\), and \(n=9\). Therefore, \(S_9=\frac{9}{2}[2(18)+(9-1)2]=\frac{9}{2}(52)=234\). Hence, 234 is correct. An answer such as 230 may result from using the wrong number of terms or making an error in the sum formula. Exam tip: identify \(a\), \(d\), and \(n\) before applying the AP formula.
Frequently asked questions
What is the correct answer to this question?
234
Why is this the correct answer?
The daily number of patients forms an arithmetic progression: \(18, 20, 22, \ldots\). Here, \(a=18\), \(d=2\), and \(n=9\). Therefore, \(S_9=\frac{9}{2}[2(18)+(9-1)2]=\frac{9}{2}(52)=234\). Hence, 234 is correct. An answer such as 230 may result from using the wrong number of terms or making an error in the sum formula. Exam tip: identify \(a\), \(d\), and \(n\) before applying the AP 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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