A geometric sequence follows the pattern:

$a, ar, ar^2, ar^3, \dots$

where each term is obtained by multiplying the previous term by the common ratio $r$.

Step 1: Find the Common Ratio $r$

To find $r$, divide any term by its preceding term:

$r = \frac{50}{250} = \frac{1}{5}$

$r = \frac{10}{50} = \frac{1}{5}$

Since the ratio is consistent, the sequence is geometric with $r = \frac{1}{5}$.