A student solves (18) questions on the first day and (4) more questions each day. On which day will he solve (102) questions?
Answer and explanation
Correct answer: 22nd day
The number of questions solved each day forms an AP with first term \(a=18\) and common difference \(d=4\). The number solved on the \(n\)th day is \(a_n=a+(n-1)d\). Thus, \(102=18+(n-1)4\), so \(84=4(n-1)\) and \(n-1=21\). Hence, \(n=22\). On the 21st day, the student solves 98 questions, so 102 questions are solved on the 22nd day. Exam tip: identify whether the question asks for a term of the AP or for the total sum.
Frequently asked questions
What is the correct answer to this question?
22nd day
Why is this the correct answer?
The number of questions solved each day forms an AP with first term \(a=18\) and common difference \(d=4\). The number solved on the \(n\)th day is \(a_n=a+(n-1)d\). Thus, \(102=18+(n-1)4\), so \(84=4(n-1)\) and \(n-1=21\). Hence, \(n=22\). On the 21st day, the student solves 98 questions, so 102 questions are solved on the 22nd day. Exam tip: identify whether the question asks for a term of the AP or for the total sum.
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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