If (a_n=6n^2-5n+2), what is (a_{n+1}-a_n)?
Answer and explanation
Correct answer: \(12n+1\)
Given \(a_n=6n^2-5n+2\), substitute \(n+1\) for \(n\): \(a_{n+1}=6(n+1)^2-5(n+1)+2=6n^2+7n+3\). Hence, \(a_{n+1}-a_n=(6n^2+7n+3)-(6n^2-5n+2)=12n+1\). Therefore, option B is correct. \(12n-5\) can result from an error while subtracting the constant terms. Exam tip: expand \((n+1)^2\) as \(n^2+2n+1\) before simplifying.
Frequently asked questions
What is the correct answer to this question?
\(12n+1\)
Why is this the correct answer?
Given \(a_n=6n^2-5n+2\), substitute \(n+1\) for \(n\): \(a_{n+1}=6(n+1)^2-5(n+1)+2=6n^2+7n+3\). Hence, \(a_{n+1}-a_n=(6n^2+7n+3)-(6n^2-5n+2)=12n+1\). Therefore, option B is correct. \(12n-5\) can result from an error while subtracting the constant terms. Exam tip: expand \((n+1)^2\) as \(n^2+2n+1\) before simplifying.
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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