If (a_n=8n^2-7n+4), what is (a_{n+1}-a_n)?
Answer and explanation
Correct answer: \(16n+1\)
Given \(a_n=8n^2-7n+4\), substitute \(n+1\) for \(n\): \(a_{n+1}=8(n+1)^2-7(n+1)+4=8n^2+9n+5\). Therefore, \(a_{n+1}-a_n=(8n^2+9n+5)-(8n^2-7n+4)=16n+1\). The option \(16n-7\) results from incorrectly handling the linear term produced when expanding \((n+1)^2\). Exam tip: find \(a_{n+1}\) completely before subtracting \(a_n\).
Frequently asked questions
What is the correct answer to this question?
\(16n+1\)
Why is this the correct answer?
Given \(a_n=8n^2-7n+4\), substitute \(n+1\) for \(n\): \(a_{n+1}=8(n+1)^2-7(n+1)+4=8n^2+9n+5\). Therefore, \(a_{n+1}-a_n=(8n^2+9n+5)-(8n^2-7n+4)=16n+1\). The option \(16n-7\) results from incorrectly handling the linear term produced when expanding \((n+1)^2\). Exam tip: find \(a_{n+1}\) completely before subtracting \(a_n\).
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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