In sports practice, running time is (15) minutes on the first day and increases by (5) minutes each next day. What is the running time on the (7)th day?
Answer and explanation
Correct answer: 45 minutes
The running times 15, 20, 25, ... form an arithmetic progression (AP), with first term \(a=15\) and common difference \(d=5\). The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_7=15+(7-1)\times5=45\) minutes. Choosing 50 minutes would give the time for the eighth day, not the seventh. Exam tip: in the \(n\)th-term formula of an AP, add the common difference \(n-1\) times.
Frequently asked questions
What is the correct answer to this question?
45 minutes
Why is this the correct answer?
The running times 15, 20, 25, ... form an arithmetic progression (AP), with first term \(a=15\) and common difference \(d=5\). The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_7=15+(7-1)\times5=45\) minutes. Choosing 50 minutes would give the time for the eighth day, not the seventh. Exam tip: in the \(n\)th-term formula of an AP, add the common difference \(n-1\) times.
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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