Which term of the arithmetic progression (23,31,39,\ldots) is (111)?
Answer and explanation
Correct answer: 12th term
Here, the first term is \(a=23\) and the common difference is \(d=31-23=8\). The \(n\)th term is \(a+(n-1)d\). Thus, \(23+(n-1)\times 8=111\) gives \((n-1)=11\), so \(n=12\). Therefore, 111 is the 12th term. The 11th term is \(23+10\times8=103\), so it is not correct. Exam tip: identify \(a\) and \(d\) first, then equate the given value to \(a_n\).
Frequently asked questions
What is the correct answer to this question?
12th term
Why is this the correct answer?
Here, the first term is \(a=23\) and the common difference is \(d=31-23=8\). The \(n\)th term is \(a+(n-1)d\). Thus, \(23+(n-1)\times 8=111\) gives \((n-1)=11\), so \(n=12\). Therefore, 111 is the 12th term. The 11th term is \(23+10\times8=103\), so it is not correct. Exam tip: identify \(a\) and \(d\) first, then equate the given value to \(a_n\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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