Question

He first term in the sequence is 1, and each other term is 5 more than three times the previous term. 1, , , , Blank 1: Blank 2: Blank 3: Blank 4:

Answer 1

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

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:

`a_(n)=3a_(n-1)+5`

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

`a_(2)=3a_(2-1)+5 = 3a_(1)+5=(3* 1)+5=8\\\\a_(3)=3a_(3-1)+5 = 3a_(2)+5=(3* 8)+5=29\\\\a_(4)=3a_(4-1)+5 = 3a_(3)+5=(3* 29)+5=92\\\\a_(5)=3a_(5-1)+5 = 3a_(4)+5=(3* 92)+5=281`

Thus, the complete sequence is:

1, 8, 29, 92, 281.