In the sequence (23,38,53,68,\ldots), which term is (218)?
Answer and explanation
Correct answer: 14th term
This is an arithmetic progression with first term \(a=23\) and common difference \(d=15\). Its \(n\)th term is \(a_n=a+(n-1)d\). So, \(23+(n-1)\times15=218\) gives \((n-1)\times15=195\), hence \(n-1=13\) and \(n=14\). Therefore, 218 is the 14th term. The 13th term is \(203\), not 218. Exam tip: While finding a term number, remember that the formula contains \(n-1\).
Frequently asked questions
What is the correct answer to this question?
14th term
Why is this the correct answer?
This is an arithmetic progression with first term \(a=23\) and common difference \(d=15\). Its \(n\)th term is \(a_n=a+(n-1)d\). So, \(23+(n-1)\times15=218\) gives \((n-1)\times15=195\), hence \(n-1=13\) and \(n=14\). Therefore, 218 is the 14th term. The 13th term is \(203\), not 218. Exam tip: While finding a term number, remember that the formula contains \(n-1\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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