Respuesta :
Answer:
[tex]a_n=5+2n[/tex]
Step-by-step explanation:
Each term is 2 more than the previous term, so the common difference is 2.
Let [tex]a_n[/tex] be the nth term of the sequence. Then, the first term is [tex]a_1=7[/tex].
The second term is [tex]a_2=7+2=9[/tex], and the third term is [tex]a_3=7+2+2=11[/tex].
Therefore, every term can be written as
[tex]a_n=7+\underbrace{2+2\cdots +2}_{n-1~\text{times}}[/tex].
Since repeated addition is multiplication, this can be written as
[tex]a_n=7+2(n-1),[/tex]
which is the nth term rule of the linear sequence.
This could also be expanded to [tex]\boxed{a_n=5+2n.}[/tex]
