The arithmetic sequence is ...

Find the common difference by subtracting successive terms.

The common difference is –4.

Subtract 4 to last term of the sequence to get the next termin the sequence.

Continue subtracting 4 untill the next three terms are found.

–3 – 4 = –7, –7 – 4 = –11 and –11 – 4 = –15.

The next three terms are –7, –11, –15.