Which is the first negative term of the AP (105,98,91,\ldots)?
Answer and explanation
Correct answer: 17th term
Here, the first term is \(a=105\) and the common difference is \(d=98-105=-7\). Therefore, \(a_n=a+(n-1)d=105-7(n-1)=112-7n\). For a negative term, \(112-7n<0\), so \(n>16\). The 16th term is \(0\), which is not negative; hence the 17th term, \(-7\), is the first negative term. Exam tip: For a negative term use \(<0\), not \(\leq0\).
Frequently asked questions
What is the correct answer to this question?
17th term
Why is this the correct answer?
Here, the first term is \(a=105\) and the common difference is \(d=98-105=-7\). Therefore, \(a_n=a+(n-1)d=105-7(n-1)=112-7n\). For a negative term, \(112-7n<0\), so \(n>16\). The 16th term is \(0\), which is not negative; hence the 17th term, \(-7\), is the first negative term. Exam tip: For a negative term use \(<0\), not \(\leq0\).
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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