In the arithmetic progression (22,27,32,\ldots), if (a_n=87), what is (n)?
Answer and explanation
Correct answer: 14
Here, the first term is 22 and the common difference is 5. Thus, the nth term is \(a_n=22+(n-1)\times5\). Substituting \(a_n=87\), we get \(22+5(n-1)=87\), so \(5(n-1)=65\), \(n-1=13\), and \(n=14\). Therefore, 87 is the 14th term of the AP. If 13 is chosen, the term would be \(82\), not 87. Exam tip: while finding a term number, handle the \(n-1\) carefully.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
Here, the first term is 22 and the common difference is 5. Thus, the nth term is \(a_n=22+(n-1)\times5\). Substituting \(a_n=87\), we get \(22+5(n-1)=87\), so \(5(n-1)=65\), \(n-1=13\), and \(n=14\). Therefore, 87 is the 14th term of the AP. If 13 is chosen, the term would be \(82\), not 87. Exam tip: while finding a term number, handle the \(n-1\) carefully.
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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