A student studies for (27) minutes on the first day and (6) more minutes each day. On which day will he study for (165) minutes?
Answer and explanation
Correct answer: 24th day
The daily study times form an arithmetic progression with first term \(a=27\) and common difference \(d=6\). The study time on the \(n\)th day is \(a_n=a+(n-1)d\). Thus, \(165=27+(n-1)\times6\), so \(138=6(n-1)\) and \(n-1=23\). Hence, \(n=24\), meaning the student will study for 165 minutes on the 24th day. On the 23rd day, the time would be only \(159\) minutes. Exam tip: While finding a term number, remember that the AP formula contains \(n-1\).
Frequently asked questions
What is the correct answer to this question?
24th day
Why is this the correct answer?
The daily study times form an arithmetic progression with first term \(a=27\) and common difference \(d=6\). The study time on the \(n\)th day is \(a_n=a+(n-1)d\). Thus, \(165=27+(n-1)\times6\), so \(138=6(n-1)\) and \(n-1=23\). Hence, \(n=24\), meaning the student will study for 165 minutes on the 24th day. On the 23rd day, the time would be only \(159\) minutes. Exam tip: While finding a term number, remember that the AP formula contains \(n-1\).
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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