A student solves (55) questions on the first day and (12) more questions each day. On which day will he solve (367) questions?
Answer and explanation
Correct answer: 27th day
The number of questions solved each day forms an AP with first term \(a=55\) and common difference \(d=12\). The number solved on the \(n\)th day is \(a_n=a+(n-1)d\). Thus, \(367=55+(n-1)\times12\), giving \(312=12(n-1)\), so \(n-1=26\) and \(n=27\). Therefore, the student will solve 367 questions on the 27th day. The closest distractor, the 26th day, would give only \(355\) questions. Exam tip: Since the question asks for one day's count, use \(a_n\), not the sum formula \(S_n\).
Frequently asked questions
What is the correct answer to this question?
27th day
Why is this the correct answer?
The number of questions solved each day forms an AP with first term \(a=55\) and common difference \(d=12\). The number solved on the \(n\)th day is \(a_n=a+(n-1)d\). Thus, \(367=55+(n-1)\times12\), giving \(312=12(n-1)\), so \(n-1=26\) and \(n=27\). Therefore, the student will solve 367 questions on the 27th day. The closest distractor, the 26th day, would give only \(355\) questions. Exam tip: Since the question asks for one day's count, use \(a_n\), not the sum formula \(S_n\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
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