What is the (18)th term of the AP \(-7,\frac{-3}{2},4,\ldots\)?
Answer and explanation
Correct answer: \(\frac{173}{2}\)
The first term is \(a=-7\), and the common difference is \(d=\frac{-3}{2}-(-7)=\frac{11}{2}\). Using \(a_n=a+(n-1)d\), we get \(a_{18}=-7+17\times\frac{11}{2}=\frac{-14+187}{2}=\frac{173}{2}\). Hence, \(\frac{173}{2}\) is correct. The option \(\frac{175}{2}\) can result from a small error in counting terms or arithmetic. Exam tip: for an AP involving fractions, write terms with a common denominator first to check the common difference accurately.
Frequently asked questions
What is the correct answer to this question?
\(\frac{173}{2}\)
Why is this the correct answer?
The first term is \(a=-7\), and the common difference is \(d=\frac{-3}{2}-(-7)=\frac{11}{2}\). Using \(a_n=a+(n-1)d\), we get \(a_{18}=-7+17\times\frac{11}{2}=\frac{-14+187}{2}=\frac{173}{2}\). Hence, \(\frac{173}{2}\) is correct. The option \(\frac{175}{2}\) can result from a small error in counting terms or arithmetic. Exam tip: for an AP involving fractions, write terms with a common denominator first to check the common difference accurately.
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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