What is the rule for the pattern 69 75 81 87 93?

Answer 1

Any given rule is only valid for n = 1, 2, ..., 5.

There are infinitely many solutions; one solution is:

t{n} = (-57n⁵ + 855n⁴ - 4845n³ + 12825n² - 14898n + 14400)/120

This gives t{1, 2, ..., 5} = {69, 75, 81, 87, 93} and t6 = 42

However, the solution your teacher is most likely expecting is the much simpler:

t{n} = 6n + 63

which also gives t{1, 2, ..., 5} = {69, 75, 81, 87, 93} but t6 = 99.