If (a_n=4n^2+n), what is (a_{n+1}-a_n)?
Answer and explanation
Correct answer: \(8n+5\)
Given \(a_n=4n^2+n\), we have \(a_{n+1}=4(n+1)^2+(n+1)\). Hence, \(a_{n+1}-a_n=4[(n+1)^2-n^2]+1=4(2n+1)+1=8n+5\). Therefore, \(8n+5\) is correct. A result such as \(8n+3\) can arise from an error in expanding the constant terms. Exam tip: while finding \(a_{n+1}\), replace every occurrence of \(n\) with \(n+1\).
Frequently asked questions
What is the correct answer to this question?
\(8n+5\)
Why is this the correct answer?
Given \(a_n=4n^2+n\), we have \(a_{n+1}=4(n+1)^2+(n+1)\). Hence, \(a_{n+1}-a_n=4[(n+1)^2-n^2]+1=4(2n+1)+1=8n+5\). Therefore, \(8n+5\) is correct. A result such as \(8n+3\) can arise from an error in expanding the constant terms. Exam tip: while finding \(a_{n+1}\), replace every occurrence of \(n\) with \(n+1\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
