What is the (42)nd term of the AP \(9,\frac{23}{2},14,\ldots\)?
Answer and explanation
Correct answer: \(\frac{223}{2}\)
The first term is \(a=9\), and the common difference is \(d=\frac{23}{2}-9=\frac{5}{2}\). The nth term is \(a_n=a+(n-1)d\). Therefore, \(a_{42}=9+41\times\frac{5}{2}=\frac{18+205}{2}=\frac{223}{2}\). \(\frac{225}{2}\) can result from an incorrect count of intervals or using the wrong value in place of \(n-1\). Exam tip: always use \(n-1\), not \(n\), in the AP nth-term formula.
Frequently asked questions
What is the correct answer to this question?
\(\frac{223}{2}\)
Why is this the correct answer?
The first term is \(a=9\), and the common difference is \(d=\frac{23}{2}-9=\frac{5}{2}\). The nth term is \(a_n=a+(n-1)d\). Therefore, \(a_{42}=9+41\times\frac{5}{2}=\frac{18+205}{2}=\frac{223}{2}\). \(\frac{225}{2}\) can result from an incorrect count of intervals or using the wrong value in place of \(n-1\). Exam tip: always use \(n-1\), not \(n\), in the AP nth-term formula.
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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