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Answer and step-by-step explanation:
To make the general rule of the given sequence, find the common difference first.
Subtract each term by the previous term.
3, 6, 9, 12, ...
6 - 3 = 3
9 - 6 = 3
12 - 9 = 3
Thus, the common difference is 3.
It can also be represented as
where
an is the nth term,
n is the number of terms, and
3 is the common difference.
You can check by finding the 4th term which is already in the given sequence.
a4 = 12
a4 = 3(4)
a4 = 12
12 = 12
Thus, the general rule is correct.