In an AP, (a_1=52) and (d=-4). What is the first (n) for which (a_n) is negative?
Answer and explanation
Correct answer: 15
The nth term of an AP is \(a_n=a_1+(n-1)d\). Thus, \(a_n=52+(n-1)(-4)=56-4n\). For a negative term, \(56-4n<0\), so \(n>14\). The smallest integer satisfying this is \(n=15\), and hence \(a_{15}=-4\) is the first negative term. At \(n=14\), the term is \(0\), which is not negative. Exam tip: when the question asks for the “first” term, choose the smallest integer greater than the value obtained from the inequality.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
The nth term of an AP is \(a_n=a_1+(n-1)d\). Thus, \(a_n=52+(n-1)(-4)=56-4n\). For a negative term, \(56-4n<0\), so \(n>14\). The smallest integer satisfying this is \(n=15\), and hence \(a_{15}=-4\) is the first negative term. At \(n=14\), the term is \(0\), which is not negative. Exam tip: when the question asks for the “first” term, choose the smallest integer greater than the value obtained from the inequality.
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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