Respuesta :
Answer:
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.
