Question

Which of the following are geometric sequences?Check all that apply.
A. 2, -2, 2, -2, 2, -2, 2
B. 1, 2, 4, 8, 16, 32
C. 1, 4, 9, 16, 25, 36, 49
D. 10, 5, 2.5, 1.25, 0.625, 0.3125

Answer 1

first one is
\[2\times (-1)^{n+1}\] go geometric. notice that each ratio is -1

Answer 2

second one is
\[2^{n-1}\] also geometric. notice again that common ratio is 2

Answer 3

third one is
\[n^2\] not geometric because for example
\[\frac{25}{16}\neq \frac{36}{25}\]

Answer 4

last one ... take the ratio of any two successive terms. if those ratios are the same, then it is geometric.