In the AP (73,65,57,\ldots), which is the first term less than (-80)?
Answer and explanation
Correct answer: (-87)
For this AP, the first term is \(a=73\) and the common difference is \(d=65-73=-8\). Thus, \(a_n=73-8(n-1)\). Here \(a_{20}=-79\), which is greater than \((-80)\), while the next term \(a_{21}=-87\) is less than \((-80)\). Therefore, the first such term is \((-87)\). Exam tip: In a decreasing AP, check the two consecutive terms around the given boundary to identify the first required term.
Frequently asked questions
What is the correct answer to this question?
(-87)
Why is this the correct answer?
For this AP, the first term is \(a=73\) and the common difference is \(d=65-73=-8\). Thus, \(a_n=73-8(n-1)\). Here \(a_{20}=-79\), which is greater than \((-80)\), while the next term \(a_{21}=-87\) is less than \((-80)\). Therefore, the first such term is \((-87)\). Exam tip: In a decreasing AP, check the two consecutive terms around the given boundary to identify the first required 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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