Question

When is a sequence geometric?

Answer 1

When you multiply and divide the numbers like:

\(\large\color{blue}{ 1,~2,~4,~8,~16.... }\) (you can see you are multiplying by 2 every time)
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\(\large\color{blue}{ 625,~125,~25,~5,~1.... }\) (you can see you are multiplying by 1/5 every time (i.e. dividing by 5))

Answer 2

(Arithmetic sequence would be adding/subtracting)

Answer 3

when it looks like
\[a,ar,ar^2,ar^3,ar^4,...\] for example
\[a=2,r=3\]
\[2,2\times 3,2\times 3^2,2\times 3^3,2\times 3^4,...\]