Question

How do I find the $n^{\mathrm{th}}$ term of the arithmetic sequence whose initial term and common difference $d$ are given below?

$a_1=4$, $d=3$

Answer 1

Find $n^{\mathrm{th}}$ term:

Arithmetic sequence for $n^{\mathrm{th}}$ term with initial term $a_1$ and common difference $d$ is given by $a_n=a_1+\left(n-1\right)d$.

Substituting $a_1=4$ and $d=3$ in $a_n=a_1+\left(n-1\right)d$.

$$\begin{gathered} \Rightarrow a_n=4+\left(n-1\right)3 \\ \Rightarrow a_n=4+3n-3 \\ \therefore a_n=3n+1 \end{gathered}$$

Hence, $n^{\mathrm{th}}$ is $a_n=3n+1$, where $n\in \mathrm{\mathbb{N}}$.