What is the (17)th term of the AP (15,22,29,36,\ldots)?
Answer and explanation
Correct answer: \(127\)
The first term of this AP is \(a=15\), and the common difference is \(d=22-15=7\). The \(n\)th term is given by \(a_n=a+(n-1)d\). Therefore, \(a_{17}=15+(17-1)\times7=15+112=127\). Hence, \(127\) is correct. Getting \(125\) usually results from counting the number of differences incorrectly; there are \(16\) differences up to the 17th term. Exam tip: always use \(n-1\), not \(n\), in the nth-term formula.
Frequently asked questions
What is the correct answer to this question?
\(127\)
Why is this the correct answer?
The first term of this AP is \(a=15\), and the common difference is \(d=22-15=7\). The \(n\)th term is given by \(a_n=a+(n-1)d\). Therefore, \(a_{17}=15+(17-1)\times7=15+112=127\). Hence, \(127\) is correct. Getting \(125\) usually results from counting the number of differences incorrectly; there are \(16\) differences up to the 17th term. Exam tip: always use \(n-1\), not \(n\), in the 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.
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