The explicit formula for the sequence 3, 6, 9, 12, 15, ... is:
T(n) = 3n, where n is a positive integer.
Each term in the sequence is obtained by adding 3 to the previous term. So, the nth term can be written as:
T(n) = T(n-1) + 3
Starting with T(1) = 3, we can recursively apply this formula to find each term:
T(2) = T(1) + 3 = 3 + 3 = 6
T(3) = T(2) + 3 = 6 + 3 = 9
T(4) = T(3) + 3 = 9 + 3 = 12
and so on...
We can also see that each term is 3 more than (n-1) times 3:
T(n) = 3(n-1) + 3
Simplifying this formula gives:
T(n) = 3n.