Question

Write the first three terms in each of the following sequences defined by following:
$\left(i\right)a_n=2n+5\left(ii\right)a_n=\frac{n-3}{4}$

Answer 1

$\left(i\right)$ Finding sequence
Given, $a_n=2n+5$ where $n\in N$
Substitute $n=1,2,$ and $3$ in $a_n,$ we get
$a_1=2\times 1+5$
$\Rightarrow a_1=7$
$a_2=2\times 2+5$
$\Rightarrow a_2=9$
$a_3=2\times 3+5$
$\Rightarrow a_3=11$
Therefore, the required first three terms are $7,9$ and $11$.

$\left(ii\right)$ Finding sequence
Given, $a_n=\frac{n-3}{4}$ Where $n\in N$
Substitute $n=1,2,$ and $3$ in $a_n,$ we get
$a_1=\frac{1-3}{4}\Rightarrow a_1=\frac{-1}{2}$
$a_2=\frac{2-3}{4}\Rightarrow a_2=\frac{-1}{4}$
$a_3=\frac{3-3}{4}\Rightarrow a_3=0$
Therefore, the required first three terms are $\frac{-1}{2},\frac{-1}{4},0$.