Which of the following nth-term expressions represents an arithmetic progression (AP) for every positive integer n?
Advertisement
Answer and explanation
Correct answer: \(a_n=(n+1)(n+4)-n^2\)
Expanding option A gives \(a_n=n^2+5n+4-n^2=5n+4\). It has the form \(an+b\), so its common difference is the constant \(5\). Option B contains an \(n^2\) term, so successive differences cannot remain constant. Exam tip: an AP’s nth term is linear in \(n\).
Frequently asked questions
What is the correct answer to this question?
\(a_n=(n+1)(n+4)-n^2\)
Why is this the correct answer?
Expanding option A gives \(a_n=n^2+5n+4-n^2=5n+4\). It has the form \(an+b\), so its common difference is the constant \(5\). Option B contains an \(n^2\) term, so successive differences cannot remain constant. Exam tip: an AP’s nth term is linear in \(n\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
Advertisement