A tank has (240) litres of water in the first hour and (18) litres decrease every hour. How much water will be there in the (9)th hour?
Answer and explanation
Correct answer: 96 litres
The water amounts form a decreasing AP, with first term \(a=240\) and common difference \(d=-18\). Thus, \(a_9=a+(9-1)d=240+8(-18)=96\) litres. The value \(102\) litres would count only 7 decreases, whereas there are 8 decreases from the first hour to the ninth hour. Exam tip: In \(a_n=a+(n-1)d\), use \(n-1\), not \(n\).
Frequently asked questions
What is the correct answer to this question?
96 litres
Why is this the correct answer?
The water amounts form a decreasing AP, with first term \(a=240\) and common difference \(d=-18\). Thus, \(a_9=a+(9-1)d=240+8(-18)=96\) litres. The value \(102\) litres would count only 7 decreases, whereas there are 8 decreases from the first hour to the ninth hour. Exam tip: In \(a_n=a+(n-1)d\), use \(n-1\), not \(n\).
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.
