Answer:
The term rule will be:
[tex]a_n=n+21[/tex]
Step-by-step explanation:
Given the sequence
[tex]22, 23, 24, 25, ...[/tex]
Computing the common difference of all the adjacent terms
[tex]22,\:23,\:24,\:25[/tex]
[tex]23-22=1,\:\quad \:24-23=1,\:\quad \:25-24=1[/tex]
As the difference between all the adjacent terms is the same and equal to
[tex]d=1[/tex]
The first element of the sequence
[tex]a_1=22[/tex]
We know that An Arithmetic sequence has a constant difference 'd' and is defined by
[tex]a_n=a_1+\left(n-1\right)d[/tex]
substituting [tex]a_1=22[/tex], and [tex]d=1[/tex] in the nth term to get the term rule
[tex]a_n=a_1+\left(n-1\right)d[/tex]
[tex]a_n=\left(n-1\right)+22[/tex]
[tex]a_n=n+21[/tex]
Therefore, the term rule will be:
[tex]a_n=n+21[/tex]
