What is the (27)th term of the AP \(-11,\frac{-9}{2},2,\ldots\)?
Answer and explanation
Correct answer: 158
The first term is \(a=-11\), and the common difference is \(d=\frac{-9}{2}-(-11)=\frac{13}{2}\). Therefore, \(a_{27}=a+(27-1)d=-11+26\times\frac{13}{2}=-11+169=158\). Hence, 158 is correct. \(169\) represents only \(26d\); the first term \(-11\) must also be added. Exam tip: while finding the \(n\)th term, use \(a_n=a+(n-1)d\), not \(a+nd\).
Frequently asked questions
What is the correct answer to this question?
158
Why is this the correct answer?
The first term is \(a=-11\), and the common difference is \(d=\frac{-9}{2}-(-11)=\frac{13}{2}\). Therefore, \(a_{27}=a+(27-1)d=-11+26\times\frac{13}{2}=-11+169=158\). Hence, 158 is correct. \(169\) represents only \(26d\); the first term \(-11\) must also be added. Exam tip: while finding the \(n\)th term, use \(a_n=a+(n-1)d\), not \(a+nd\).
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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