The 5th term in a sequence is 27, and each term is 3 less than the previous term. Enter an explicit rule and a recursive rule to complete the description of the sequence.

Recursive Rule => a(n+1) = a(n) - 3

Explicit Rule => a(n) = 15 - (n-1)*3  

Sequence = 39, 36, 33, 30, 27

Explanation:

Recursive Rule:

Let a(n) denotes nth term and a(n-1) denotes the previous term

We are given the each successive term is 3 less than the previous term so we can write  

a(n) = a(n-1) - 3

we can also write  

Recursive Rule => a(n+1) = a(n) - 3

It still means the same. Each new term is 3 less than the previous term.

Explicit Rule:

We are also given that the 5th term a(5) is equal to 27 and we already know the difference between successive terms that is -3

a(n) = a(1) + (n-1)*d

We need the first term to specify the explicit rule

For the 5th term we can write

a(5) = a(1) + (5-1)*-3

27 = a(1) - (4)*3

27 = a(1) - 12

a(1) = 27 + 12 = 39

Explicit Rule => a(n) = 15 - (n-1)*3  

Verification:

a(1) = 39

a(2) = a(1) - (2-1)*3 = 39 - (1)*3 = 39 - 3 = 36

a(3) = a(1) - (3-1)*3 = 39 - (2)*3 = 39 - 6 = 33

a(4) = a(1) - (4-1)*3 = 39 - (3)*3 = 15 + 9 = 30

a(5) = a(1) - (5-1)*3 = 39 - (4)*3 = 15 + 12 = 27

sequence = 39, 36, 33, 30, 27

a(n) = a(n-1) - 3

a(5) = a(5-1) - 3 = a(4) - 3 = 30 - 3 = 27

a(4) = a(4-1) - 3 = a(3) - 3 = 33 - 3 = 30

a(3) = a(3-1) - 3 = a(2) - 3 = 36 - 3 = 33

a(2) = a(2-1) - 3 = a(1) - 3 = 39 - 3 = 36

a(1) = 39

sequence = 39, 36, 33, 30, 27

Conclusion:

Hence as you can see both of the rules Recursive and Explicit have being tested and verified. The obtained results are correct.

f 5 , h

glass wants to live in a world of super heroes and villains. he have lived all his life trying to be responsible for the creating the origin story of a super hero; he schemed and caused many incidents (many of them fatal) hoping that someday someone with superpowers would show up and save the day.

he knew himself very much. he saw himself as a villain of a real-life super hero story. he was aware of his strengths (more than smart enough for being manipulative and scheming) and weaknesses (having fragile bones and having to rely on his mind to succeed).