Question

Identify each sequence as geometric or not geometric.

Geometric Not Geometric
10, 5, 2.5, 1.25, ...


1
3

,
4
9

,
16
27

,
64
81



1, 4, 9, 16, ...


2, 2, 2, 2, ...

Answer 1

10, 5, 2.5, 1.25, ... — Geometric. Common ratio r = 1/2 (each term is half the previous). General term: 10*(1/2)^(n-1).

1/3, 4/9, 16/27, 64/81, ... — Geometric. Common ratio r = 4/3 (each term ×4/3). General term: (1/3)*(4/3)^(n-1).

1, 4, 9, 16, ... — Not geometric. Ratios between successive terms are 4, 9/4, 16/9, ... (not constant); this is n^2.

2, 2, 2, 2, ... — Geometric. Common ratio r = 1 (constant sequence). General term: 2*(1)^(n-1) = 2.