Question

How do you write the expression for the $n^{th}$ term of the sequence given $1,4,7,10,13.....$?

Answer 1

Finding the expression for the $n^{th}$ in the given sequence:

By observing the sequence $1,4,7,10,13.....$

First term $a=1$ and the common difference $d=3$

So the given sequence is in arithmetic Progression.

We know that,

Formula for the $n^{th}$ term of the arithmetic Progression. is

$$\begin{gathered} {\mathrm{a}}_{\mathrm{n}}=\mathrm{a}+(\mathrm{n}-1)\mathrm{d} \\ \Rightarrow {\mathrm{a}}_{\mathrm{n}}=1+(\mathrm{n}-1)\times 3\left[\because a=1;d=3\right] \\ \Rightarrow {\mathrm{a}}_{\mathrm{n}}=1+3\mathrm{n}-3 \\ \Rightarrow {\mathrm{a}}_{\mathrm{n}}=3\mathrm{n}-2 \end{gathered}$$

Hence, the $n^{th}$ term of the given expression is $a_n=3n-2$.