The first two terms of a sequence are 4 and 12. If the sequence is arithmetic, what is the next term? If the sequence is geometric, what is the next term?

Step-by-step explanation:

Case 1: 20; Case 2: 36

Case 1: arithmetic sequence

The common difference is 8. Notice that 4 + 8 = 12.

a (1) = 4; a (2) = 12; a (3) = 20; etc.

The common next term (3rd term) is 20.

Case 2: geometric sequence

The common ratio is 3. Notice that 4*3 = 12.

Multiplying this second term by the common ratio (3) results in the third term: 36.