If (a_n=kn+2) and (a_5=27), what will be the value of (a_9)?
Answer and explanation
Correct answer: 47
Given \(a_n=kn+2\). Substituting \(n=5\), \(a_5=5k+2=27\), so \(5k=25\) and \(k=5\). Now, for \(n=9\), \(a_9=9\times5+2=47\). Hence, 47 is correct. The value 45 would result from incorrectly omitting the constant term \(+2\). Exam tip: first find the unknown constant from the given term, then substitute the required value of \(n\).
Frequently asked questions
What is the correct answer to this question?
47
Why is this the correct answer?
Given \(a_n=kn+2\). Substituting \(n=5\), \(a_5=5k+2=27\), so \(5k=25\) and \(k=5\). Now, for \(n=9\), \(a_9=9\times5+2=47\). Hence, 47 is correct. The value 45 would result from incorrectly omitting the constant term \(+2\). Exam tip: first find the unknown constant from the given term, then substitute the required value of \(n\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sequences.
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