Which term of the AP (15,21,27,\ldots) is (111)?
Answer and explanation
Correct answer: 17th term
Here, the first term is \(a=15\) and the common difference is \(d=21-15=6\). The \(n\)th term is \(a_n=a+(n-1)d\). Thus, \(111=15+(n-1)\times6\), so \(96=6(n-1)\) and \(n=17\). Therefore, 111 is the 17th term. The 16th term is \(105\), so it is close but not correct. Exam tip: while finding a term number, remember that the formula contains \((n-1)\).
Frequently asked questions
What is the correct answer to this question?
17th term
Why is this the correct answer?
Here, the first term is \(a=15\) and the common difference is \(d=21-15=6\). The \(n\)th term is \(a_n=a+(n-1)d\). Thus, \(111=15+(n-1)\times6\), so \(96=6(n-1)\) and \(n=17\). Therefore, 111 is the 17th term. The 16th term is \(105\), so it is close but not correct. Exam tip: while finding a term number, remember that the formula contains \((n-1)\).
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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