Question

Which sequences are geometric? Check all that apply.

10, 7.5, 5.625, 4.21875, …
160, 40, 10, 2.5, …
20, 70, 245, 857.5, …
13, 16.5, 20, 23.5, …
5, 5.5, 6.05, 6.655, …
16, 17.1, 18.2, 19.3, …

Answer 1

Geometric sequences are those whose consecutive-term ratio is constant.

1) 10, 7.5, 5.625, 4.21875, … — geometric, r = 7.5/10 = 0.75 (= 3/4).
2) 160, 40, 10, 2.5, … — geometric, r = 40/160 = 0.25 (= 1/4).
3) 20, 70, 245, 857.5, … — geometric, r = 70/20 = 3.5 (= 7/2).
4) 13, 16.5, 20, 23.5, … — not geometric (consecutive ratios differ; this is arithmetic with difference 3.5).
5) 5, 5.5, 6.05, 6.655, … — geometric, r = 5.5/5 = 1.1 (= 11/10).
6) 16, 17.1, 18.2, 19.3, … — not geometric (consecutive ratios are not constant; this is arithmetic with difference 1.1).

So sequences 1, 2, 3 and 5 are geometric.