The service cost of a vehicle is (2000) rupees in the first year and increases by (500) rupees each next year. What is the cost in the (5)th year?
Answer and explanation
Correct answer: ₹4000
The service costs form an AP with first term ₹2000 and common difference ₹500. The cost in the fifth year is \(a_5=a+(5-1)d=2000+4\times500=4000\). Hence, ₹4000 is correct. Choosing ₹4500 incorrectly counts 5 increases; from the first year to the fifth year, there are only 4 increases. Exam tip: use \(a_n=a+(n-1)d\) for the nth term of an AP.
Frequently asked questions
What is the correct answer to this question?
₹4000
Why is this the correct answer?
The service costs form an AP with first term ₹2000 and common difference ₹500. The cost in the fifth year is \(a_5=a+(5-1)d=2000+4\times500=4000\). Hence, ₹4000 is correct. Choosing ₹4500 incorrectly counts 5 increases; from the first year to the fifth year, there are only 4 increases. Exam tip: use \(a_n=a+(n-1)d\) for the nth term of an AP.
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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