On a railway route the first station is at (12) km and each next station is (7) km farther. What is the distance of the (15)th station?
Answer and explanation
Correct answer: 110 km
The station distances form an AP with first term \(a=12\) km and common difference \(d=7\) km. The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_{15}=12+(15-1)\times7=12+98=110\) km. Hence, 110 km is correct. The value 117 km would result from incorrectly adding \(15\times7\); there are only 14 gaps after the first station. Exam tip: always use \((n-1)\) in the nth-term formula.
Frequently asked questions
What is the correct answer to this question?
110 km
Why is this the correct answer?
The station distances form an AP with first term \(a=12\) km and common difference \(d=7\) km. The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_{15}=12+(15-1)\times7=12+98=110\) km. Hence, 110 km is correct. The value 117 km would result from incorrectly adding \(15\times7\); there are only 14 gaps after the first station. Exam tip: always use \((n-1)\) in the nth-term formula.
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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