What is the \(34\)th term of the AP \(7,\frac{19}{2},12,\ldots\)?
Answer and explanation
Correct answer: \(\frac{179}{2}\)
The first term is \(a=7\), and the common difference is \(d=\frac{19}{2}-7=\frac{5}{2}\). Hence, \(a_{34}=a+(34-1)d=7+33\times\frac{5}{2}=\frac{179}{2}\). Therefore, \(\frac{179}{2}\) is correct. Getting 89 is a common error caused by not handling the denominator 2 correctly while adding 7. Exam tip: always use \(a_n=a+(n-1)d\), not \(a+nd\).
Frequently asked questions
What is the correct answer to this question?
\(\frac{179}{2}\)
Why is this the correct answer?
The first term is \(a=7\), and the common difference is \(d=\frac{19}{2}-7=\frac{5}{2}\). Hence, \(a_{34}=a+(34-1)d=7+33\times\frac{5}{2}=\frac{179}{2}\). Therefore, \(\frac{179}{2}\) is correct. Getting 89 is a common error caused by not handling the denominator 2 correctly while adding 7. Exam tip: always 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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