In the arithmetic progression (3,11,19,27,\ldots), which term is (83)?
Answer and explanation
Correct answer: 11th term
Here, the first term is \(a=3\) and the common difference is \(d=8\). The \(n\)th term is \(a_n=a+(n-1)d\). Thus, \(3+(n-1)\times8=83\), giving \((n-1)\times8=80\), so \(n=11\). Therefore, 83 is the eleventh term. The twelfth term would be \(91\), so that option is not correct. Exam tip: To find the position of a number in an AP, equate it to \(a_n\) and solve for \(n\).
Frequently asked questions
What is the correct answer to this question?
11th term
Why is this the correct answer?
Here, the first term is \(a=3\) and the common difference is \(d=8\). The \(n\)th term is \(a_n=a+(n-1)d\). Thus, \(3+(n-1)\times8=83\), giving \((n-1)\times8=80\), so \(n=11\). Therefore, 83 is the eleventh term. The twelfth term would be \(91\), so that option is not correct. Exam tip: To find the position of a number in an AP, equate it to \(a_n\) and solve for \(n\).
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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