Respuesta :

Answer:

The complete sequence is: 1, 8, 29, 92, 281.

Step-by-step explanation:

The series to be completed is:

1, _, _, _, _

The information provided is:

  • The first term in the sequence is 1.
  • Each other term is 5 more than three times the previous term.

Then the nth term can be determined using the expression:

[tex]a_{n}=3a_{n-1}+5[/tex]

Compute the 2nd, 3rd, 4th and 5th term as follows:

[tex]a_{2}=3a_{2-1}+5 = 3a_{1}+5=(3\times 1)+5=8\\\\a_{3}=3a_{3-1}+5 = 3a_{2}+5=(3\times 8)+5=29\\\\a_{4}=3a_{4-1}+5 = 3a_{3}+5=(3\times 29)+5=92\\\\a_{5}=3a_{5-1}+5 = 3a_{4}+5=(3\times 92)+5=281[/tex]

Thus, the complete sequence is:

1, 8, 29, 92, 281.