Which is the first negative term of the AP (45,40,35,\ldots)?
Answer and explanation
Correct answer: 11th term
Here, the first term is \(a=45\) and the common difference is \(d=-5\). Therefore, \(a_n=a+(n-1)d=45-5(n-1)=50-5n\). For the first negative term, \(50-5n<0\), so \(n>10\). The smallest integer satisfying this is \(11\); hence, the 11th term is the first negative term. The 10th term is \(0\), which is not negative. Exam tip: For a “first” term question, choose the smallest positive integer that satisfies the inequality.
Frequently asked questions
What is the correct answer to this question?
11th term
Why is this the correct answer?
Here, the first term is \(a=45\) and the common difference is \(d=-5\). Therefore, \(a_n=a+(n-1)d=45-5(n-1)=50-5n\). For the first negative term, \(50-5n<0\), so \(n>10\). The smallest integer satisfying this is \(11\); hence, the 11th term is the first negative term. The 10th term is \(0\), which is not negative. Exam tip: For a “first” term question, choose the smallest positive integer that satisfies 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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
