What is the (23)rd term of the AP \(-9,\frac{-7}{2},2,\ldots\)?
Answer and explanation
Correct answer: 112
The first term is \(a=-9\). The common difference is \(d=\frac{-7}{2}-(-9)=\frac{11}{2}\). Therefore, \(a_{23}=a+(23-1)d=-9+22\times\frac{11}{2}=-9+121=112\). Hence, the correct answer is 112. \(\frac{225}{2}\) may result from not subtracting \(-9\) correctly at the final step. Exam tip: use \(n-1\), not \(n\), in the formula for the \(n\)th term.
Frequently asked questions
What is the correct answer to this question?
112
Why is this the correct answer?
The first term is \(a=-9\). The common difference is \(d=\frac{-7}{2}-(-9)=\frac{11}{2}\). Therefore, \(a_{23}=a+(23-1)d=-9+22\times\frac{11}{2}=-9+121=112\). Hence, the correct answer is 112. \(\frac{225}{2}\) may result from not subtracting \(-9\) correctly at the final step. Exam tip: use \(n-1\), not \(n\), in the formula for the \(n\)th 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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