In the AP (260,245,230,\ldots), which is the first term less than (-100)?
Answer and explanation
Correct answer: (-115)
In this AP, the first term is 260 and the common difference is \(d=-15\). \((-100)\) is itself a term of the AP, since \(260-15\times 24=-100\). As each successive term decreases by 15, the term after \((-100)\) is \((-100)-15=-115\). Therefore, the first term less than \((-100)\) is \((-115)\). Although \((-130)\) is also less than \((-100)\), it occurs later. Exam tip: when asked for the “first” term beyond a boundary, check the term immediately after the boundary term.
Frequently asked questions
What is the correct answer to this question?
(-115)
Why is this the correct answer?
In this AP, the first term is 260 and the common difference is \(d=-15\). \((-100)\) is itself a term of the AP, since \(260-15\times 24=-100\). As each successive term decreases by 15, the term after \((-100)\) is \((-100)-15=-115\). Therefore, the first term less than \((-100)\) is \((-115)\). Although \((-130)\) is also less than \((-100)\), it occurs later. Exam tip: when asked for the “first” term beyond a boundary, check the term immediately after the boundary term.
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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