In a hospital, (10) patients come on the first day and (2) more patients come each next day. How many patients come in (12) days?
Answer and explanation
Correct answer: 252
The daily patient counts form an arithmetic progression: 10, 12, 14, \ldots. Here, \(a=10\), \(d=2\), and \(n=12\). Therefore, \(S_{12}=\frac{12}{2}[2(10)+11(2)]=6(42)=252\). Hence, the correct answer is 252. The value 264 is the number of patients on the 12th day, \(a_{12}\), not the total over 12 days. Exam tip: distinguish between \(a_n\) for one term and \(S_n\) for the sum of terms.
Frequently asked questions
What is the correct answer to this question?
252
Why is this the correct answer?
The daily patient counts form an arithmetic progression: 10, 12, 14, \ldots. Here, \(a=10\), \(d=2\), and \(n=12\). Therefore, \(S_{12}=\frac{12}{2}[2(10)+11(2)]=6(42)=252\). Hence, the correct answer is 252. The value 264 is the number of patients on the 12th day, \(a_{12}\), not the total over 12 days. Exam tip: distinguish between \(a_n\) for one term and \(S_n\) for the sum of terms.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
