Find the (18)th term of the AP (2,11,20,29,\ldots).
Answer and explanation
Correct answer: \(155\)
For this AP, the first term is \(a=2\) and the common difference is \(d=11-2=9\). The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_{18}=2+(18-1)\times9=2+153=155\). Hence, \(155\) is correct. \(153\) is only \(17\times9\); the first term \(2\) must also be added. Exam tip: use \(n-1\), not \(n\), in the formula for the \(n\)th term.
Frequently asked questions
What is the correct answer to this question?
\(155\)
Why is this the correct answer?
For this AP, the first term is \(a=2\) and the common difference is \(d=11-2=9\). The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_{18}=2+(18-1)\times9=2+153=155\). Hence, \(155\) is correct. \(153\) is only \(17\times9\); the first term \(2\) must also be added. Exam tip: use \(n-1\), not \(n\), in the formula for the \(n\)th term.
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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