Final answer:
The correct formula for the arithmetic sequence (-7, -2, 3, 8, 13, ...) is option 2) an = 5n - 12, as the sequence increases by a common difference of 5, which is calculated by using the formula an = a1 + (n - 1) * d.
Step-by-step explanation:
To identify the correct formula for the given sequence (-7, -2, 3, 8, 13, ...), we notice that each term increases by 5 from the previous one. This suggests that the sequence is arithmetic, with a common difference of 5. The nth term of an arithmetic sequence is given by an = a1 + (n - 1) * d, where a1 is the first term and d is the common difference.
To find the first term, a1, we take the first number in the sequence which is -7. The common difference, d, is 5. Plugging these values into our formula yields an = -7 + (n - 1) * 5.
This simplifies to an = 5n - 12, as follows:
an = -7 + 5n - 5an = 5n - 12.
Hence, the correct formula is option 2) an = 5n - 12.