Final answer:
The explicit formula for the given sequence is an = 10n + 2 and the recursive formula is an = an-1 + 100.
Step-by-step explanation:
The given sequence is: 12, 112, 212, 312, 412.
To find the explicit formula, we observe that the tens digit increases by 1 and the units digit stays the same. Therefore, the explicit formula is:
an = 10n + 2
where n represents the position of the term in the sequence starting from 1.
To find the recursive formula, we observe that each term is obtained by adding 100 to the previous term. Therefore, the recursive formula is:
an = an-1 + 100