Question

Determine whether the sequence converges or diverges. If it converges, give the limit. 4, 12, 36, 108, ..

Answer 1

Answer: Diverges

Each time we multiply by 3 to get the next term

4*3 = 12

12*3 = 36

36*3 = 108

The sequence grows without bound. In other words, it does not approach a finite value. The common ratio is r = 3, which makes -1 < r < 1 false, so that is an algebraic way to see why the sequence diverges.