What will be the (31)st term of the AP (6,10,14,18,\ldots)?
Answer and explanation
Correct answer: 126
In this AP, the first term is \(a=6\) and the common difference is \(d=10-6=4\). The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_{31}=6+(31-1)\times4=6+120=126\). Choosing 122 would correspond to adding only 29 differences, so it is close to the 30th term. Exam tip: use \(n-1\), not \(n\), when finding the \(n\)th term.
Frequently asked questions
What is the correct answer to this question?
126
Why is this the correct answer?
In this AP, the first term is \(a=6\) and the common difference is \(d=10-6=4\). The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_{31}=6+(31-1)\times4=6+120=126\). Choosing 122 would correspond to adding only 29 differences, so it is close to the 30th term. Exam tip: use \(n-1\), not \(n\), when finding 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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