The service cost of a vehicle is (1500) rupees in the first year and increases by (400) rupees each next year. What is the cost in the (5)th year?
Answer and explanation
Correct answer: 3100 rupees
The service costs form an arithmetic progression with first term \(a=1500\) and common difference \(d=400\). The fifth-year cost is \(a_5=a+(5-1)d=1500+4\times400=3100\) rupees. Choosing 2900 would count only three increases, but there are four intervals from the first year to the fifth year. Exam tip: Use \(a_n=a+(n-1)d\) and count the intervals carefully.
Frequently asked questions
What is the correct answer to this question?
3100 rupees
Why is this the correct answer?
The service costs form an arithmetic progression with first term \(a=1500\) and common difference \(d=400\). The fifth-year cost is \(a_5=a+(5-1)d=1500+4\times400=3100\) rupees. Choosing 2900 would count only three increases, but there are four intervals from the first year to the fifth year. Exam tip: Use \(a_n=a+(n-1)d\) and count the intervals carefully.
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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