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If (a_n=3n^2+5n), what is (a_{n+1}-a_n)?
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Answer and explanation
Correct answer: \(6n+8\)
Here, \(a_{n+1}=3(n+1)^2+5(n+1)=3n^2+11n+8\). Therefore, \(a_{n+1}-a_n=(3n^2+11n+8)-(3n^2+5n)=6n+8\). The option \(6n+6\) results from an incorrect calculation of the constant term. Exam tip: Substitute \(n+1\), expand every bracket, and then subtract \(a_n\).
Frequently asked questions
What is the correct answer to this question?
\(6n+8\)
Why is this the correct answer?
Here, \(a_{n+1}=3(n+1)^2+5(n+1)=3n^2+11n+8\). Therefore, \(a_{n+1}-a_n=(3n^2+11n+8)-(3n^2+5n)=6n+8\). The option \(6n+6\) results from an incorrect calculation of the constant term. Exam tip: Substitute \(n+1\), expand every bracket, and then subtract \(a_n\).
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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