Recognizing Geometric Sequences

We want to identify the given sequence as arithmetic, geometric, or neither. To do so we will calculate the difference and ratio between consecutive terms. The four terms given in the graph are $2,$ $10,$ $50,$ and $250.$

We can see above that the differences are not the same. However the ratios are the same. Therefore, the given sequence is a geometric sequence with a common ratio of $5.$