If the (18)th term of the AP (b-3,b+2,b+7,\ldots) is (94), what is the value of (b)?
Answer and explanation
Correct answer: 12
The common difference between consecutive terms is \(5\), so the first term is \(a=b-3\) and \(d=5\). The \(18\)th term is \(a_{18}=a+17d\). Thus, \(94=(b-3)+17\times5=b+82\), which gives \(b=12\). If \(b=11\), the \(18\)th term would be \(93\), so it is not correct. Exam tip: use \(n-1\) common differences when finding the \(n\)th term.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The common difference between consecutive terms is \(5\), so the first term is \(a=b-3\) and \(d=5\). The \(18\)th term is \(a_{18}=a+17d\). Thus, \(94=(b-3)+17\times5=b+82\), which gives \(b=12\). If \(b=11\), the \(18\)th term would be \(93\), so it is not correct. Exam tip: use \(n-1\) common differences 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.
