Geometric because there is a common ratio of (1/4)
Step-by-step explanation:
To determine if a series is arithmetic there must be a common difference. A common difference is when you take consecutive terms and find the difference (10 - 40 = -30). Then to see if it holds true you apply it to the next term (10 - 30 = -20). If they match, then there is a common difference. In this case they do not match thus no common difference.
If it is geometric, then there is a common ratio. A common ratio is when you divide the second term from the first (10/40 = 1/4). Once you have the possible ratio you multiply the second term by the common ratio to see if it holds (10 * 1/4 = 5/2). In this case it does hold, and thus a common ratio, and a geometric sequence.
