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If (a_n=5n^2+2n-9), what is (a_{n+2}-a_n)?
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Answer and explanation
Correct answer: \(20n+24\)
Given \(a_n=5n^2+2n-9\), \(a_{n+2}=5(n+2)^2+2(n+2)-9=5n^2+22n+15\). Hence, \(a_{n+2}-a_n=(5n^2+22n+15)-(5n^2+2n-9)=20n+24\). The option \(20n+22\) results from an error in calculating the constant term. Exam tip: first expand \((n+2)^2=n^2+4n+4\) carefully.
Frequently asked questions
What is the correct answer to this question?
\(20n+24\)
Why is this the correct answer?
Given \(a_n=5n^2+2n-9\), \(a_{n+2}=5(n+2)^2+2(n+2)-9=5n^2+22n+15\). Hence, \(a_{n+2}-a_n=(5n^2+22n+15)-(5n^2+2n-9)=20n+24\). The option \(20n+22\) results from an error in calculating the constant term. Exam tip: first expand \((n+2)^2=n^2+4n+4\) carefully.
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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