Question

Find the next three terms of the sequence. Then write a rule for the sequence.

648, 216, 72, 24

Answer 1

216 is 648/3
72 is 216/3
24 is 72/3
etc

Answer 2

Test the sequence to see if it's an arithmetic sequence.
Subtract each term from the next term.

216 - 648 = 432
72 - 216 = 144
Since the differences are not the same, there is no common difference. That means the sequence is not an arithmetic sequence.

Now test the sequence for a geometric sequence.
Divide each term by the previous term.

24/72 = 1/3
72/216 = 1/3
216/648 = 1/3
Since all the divisions give the same result, there is a common factor between terms. That means it's a geometric sequence. Each term is one-third of the previous term. Now you can use that to find the next three terms.