Which term of the arithmetic progression (15,21,27,\ldots) is (105)?
Answer and explanation
Correct answer: 16th term
For this AP, the first term is \(a=15\) and the common difference is \(d=6\). The \(n\)th term is \(a_n=a+(n-1)d\). Thus, \(105=15+(n-1)\times6\), so \(n-1=15\) and \(n=16\). Therefore, 105 is the 16th term. The 15th term is \(15+14\times6=99\), so it is not correct. Exam tip: do not forget the \(n-1\) in the AP term formula.
Frequently asked questions
What is the correct answer to this question?
16th term
Why is this the correct answer?
For this AP, the first term is \(a=15\) and the common difference is \(d=6\). The \(n\)th term is \(a_n=a+(n-1)d\). Thus, \(105=15+(n-1)\times6\), so \(n-1=15\) and \(n=16\). Therefore, 105 is the 16th term. The 15th term is \(15+14\times6=99\), so it is not correct. Exam tip: do not forget the \(n-1\) in the AP term formula.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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