If (a_n=4n^2+n-6), what is (a_{n+2}-a_n)?
Answer and explanation
Correct answer: \(16n+18\)
Given \(a_n=4n^2+n-6\), substitute \(n+2\) for \(n\): \(a_{n+2}=4(n+2)^2+(n+2)-6=4n^2+17n+12\). Hence, \(a_{n+2}-a_n=(4n^2+17n+12)-(4n^2+n-6)=16n+18\). Option B results from an incorrect expansion or simplification of the constant terms. Exam tip: replace every occurrence of \(n\) with \(n+2\) before expanding the expression.
Frequently asked questions
What is the correct answer to this question?
\(16n+18\)
Why is this the correct answer?
Given \(a_n=4n^2+n-6\), substitute \(n+2\) for \(n\): \(a_{n+2}=4(n+2)^2+(n+2)-6=4n^2+17n+12\). Hence, \(a_{n+2}-a_n=(4n^2+17n+12)-(4n^2+n-6)=16n+18\). Option B results from an incorrect expansion or simplification of the constant terms. Exam tip: replace every occurrence of \(n\) with \(n+2\) before expanding the expression.
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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