### Theory:

A sequence is a function defined on the set of natural numbers $$\mathbb{N}$$. A sequence is a function of  form $f:\mathrm{ℕ}\to \mathrm{ℝ}$, where $$\mathbb{R}$$ is the set of all real numbers.
If the sequence is of the form  $$a_1$$, $$a_2$$, $$a_3$$, $$a_4$$,.... then we can associate the function to the sequence $$a_1$$, $$a_2$$, $$a_3$$, $$a_4$$,.. by $$f (n) = a_n$$, $$n = 1,2,3,$$… Let us solve a problem of sequence with a function to understand this concept.
Example:
The general term of a sequence is defined as $f\left(n\right)={a}_{n}=\frac{3n+5}{n+7}$. Find the first three terms $$a_1$$, $$a_2$$, ${a}_{3}$.

Let us substitute the natural number $$n = 1, 2, 3, 4,..$$ in the given equation.

The first three terms are:

$f\left(n\right)={a}_{n}=\frac{3n+5}{n+7}$, where $$n = 1, 2, 3, 4,..$$.

$\begin{array}{l}{a}_{1}=\frac{3\left(1\right)+5}{1+7}\\ \\ =\frac{3+5}{8}\\ \\ {a}_{1}=\frac{8}{8}\end{array}$

$\begin{array}{l}{a}_{2}=\frac{3\left(2\right)+5}{2+7}\\ \\ =\frac{6+5}{9}\\ \\ {a}_{2}=\frac{11}{9}\end{array}$

$\begin{array}{l}{a}_{3}=\frac{3\left(3\right)+5}{3+7}\\ \\ =\frac{9+5}{10}\\ \\ {a}_{3}=\frac{14}{10}\end{array}$

Therefore, the first three terms are:
• $$a_ 1=$$ $\frac{8}{8}$,
• $$a_ 2=$$ $\frac{11}{9}$,
• ${a}_{3}$ $$=$$ $\frac{14}{10}$.