In the AP (17,24,31,\ldots), (a_n=136). Find the value of (n).
Answer and explanation
Correct answer: 18
Here, the first term is \(a=17\) and the common difference is \(d=24-17=7\). The \(n\)th term is given by \(a_n=a+(n-1)d\). Thus, \(136=17+(n-1)\times7\), so \(119=7(n-1)\). Hence, \(n-1=17\) and \(n=18\). Option 17 is incorrect because the 17th term is \(129\). 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?
18
Why is this the correct answer?
Here, the first term is \(a=17\) and the common difference is \(d=24-17=7\). The \(n\)th term is given by \(a_n=a+(n-1)d\). Thus, \(136=17+(n-1)\times7\), so \(119=7(n-1)\). Hence, \(n-1=17\) and \(n=18\). Option 17 is incorrect because the 17th term is \(129\). 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.
