3,12,33,72,135

The sequence given is 3, 12, 33, 72, 135. To find the pattern, we *yze the differences between consecutive terms:

The second differences increase by 6 each time, indicating a cubic relationship. We hypothesize the nth term as (an^3 + bn^2 + cn + d). Solving the system of equations for (n = 1, 2, 3, 4, 5), we find:

[

a = 1, quad b = 0, quad c = 2, quad d = 0

]

Thus, the nth term formula is:

[

n^3 + 2n

]

Verification for the given terms confirms this formula. The next term for (n = 6) is:

[

6^3 + 2

imes 6 = 216 + 12 = 228

]

Answer: The next term in the sequence is (boxed{228}).