If (a_n=7n-13), what is (a_{4n+1})?
Answer and explanation
Correct answer: \(28n-6\)
Given \(a_n=7n-13\). To find \(a_{4n+1}\), substitute the complete index \(4n+1\) for \(n\): \(a_{4n+1}=7(4n+1)-13=28n+7-13=28n-6\). Hence, \(28n-6\) is correct. In \(28n-13\), the effect of the \(+1\) in the index has been omitted. Exam tip: always put a compound subscript in brackets before substituting it into the nth-term formula.
Frequently asked questions
What is the correct answer to this question?
\(28n-6\)
Why is this the correct answer?
Given \(a_n=7n-13\). To find \(a_{4n+1}\), substitute the complete index \(4n+1\) for \(n\): \(a_{4n+1}=7(4n+1)-13=28n+7-13=28n-6\). Hence, \(28n-6\) is correct. In \(28n-13\), the effect of the \(+1\) in the index has been omitted. Exam tip: always put a compound subscript in brackets before substituting it into the nth-term formula.
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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