Question

Which of the following can be the $n$th term of an AP?

• A. $n^3+1$
• B. $4n+3$
• C. $3n^2+5$
• D. None of these

Answer 1

The correct option is B

$4n+3$

Determine the correct Option.

The explanation for the correct option:

Option (B): Determine the $n\mathrm{th}$ term of an AP.

The formula for AP is $a_n=a_1+\left(n-1\right)d$, which is a linear relation in $n$.

The expression $4n+3$ is also linear so it can be the $n\mathrm{th}$ term of AP.

Hence, option (B) is correct.

Explanation for the incorrect option:

Option (A): The expressions $n^3+1$ is not linear relations. So, Option A is incorrect

Option (C):The expressions $3n^2+5$ is not linear relations. So, Option A is incorrect

Option (D): since one of the options is correct, So, Option D is incorrect

Therefore, options (A), (C), and (D) are incorrect.

Hence, option (B) is correct.