Respuesta :

Consecutive terms differ by 3, so

[tex]a_n=a_{n-1}+3=a_{n-2}+2\times3=a_{n-3}+3\times3=\cdots=a_1+(n-1)\times3[/tex]

Since the first term is [tex]a_1=5[/tex], the formula for the sequence is

[tex]a_n=5+3(n-1)=3n+2[/tex]