Which of the following expressions does not represent the $n$th term of an arithmetic progression for every positive integer $n$?

Question

Class 10 Mathematics Arithmetic Progressions (AP)Finding the $n$th term of an APHardLevel 66

Which of the following expressions does not represent the $n$th term of an arithmetic progression for every positive integer $n$?

Answer and explanation

Correct answer: $n^2+1$

The nth term of an AP has the form $a_n=a+(n-1)d$, so it is linear in $n$. In $n^2+1$, consecutive differences are 3, 5, 7, ..., not constant. $5$ is still an AP with $d=0$. Exam tip: a squared or cubed $n$ usually rules out an AP.

Frequently asked questions

What is the correct answer to this question?

$n^2+1$

Why is this the correct answer?

The nth term of an AP has the form $a_n=a+(n-1)d$, so it is linear in $n$. In $n^2+1$, consecutive differences are 3, 5, 7, ..., not constant. $5$ is still an AP with $d=0$. Exam tip: a squared or cubed $n$ usually rules out an AP.

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.

Report question

Which of the following expressions does not represent the \(n\)th term of an arithmetic progression for every positive integer \(n\)?

Answer and explanation

Tags

Frequently asked questions

Which of the following expressions does not represent the \(n\)th term of an arithmetic progression for every positive integer \(n\)?

Answer and explanation

Tags

Frequently asked questions

Analytics choices