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An arithmetic sequence is a list of numbers with a distinctive feature: the difference between two successive terms is always the same. This static difference is known as the common difference. In other words, if you add a particular constant number to a term in an arithmetic sequence, you'll arrive at the next term. For instance, in the sequence \(2, 4, 6, 8, \dots\), the common difference is 2.

To verify if a sequence is an arithmetic sequence, you should subtract any term from the one that follows it. Do this for multiple pairs of terms to ensure the difference remains constant. If the differences vary, the sequence isn't arithmetic. Let's look at the original exercise sequence \(3,15,75,375, \dots\). Calculating the difference between the terms \(15 - 3 = 12\), \(75 - 15 = 60\), and \(375 - 75 = 300\) results in differences that are not equal. Hence, this sequence isn't an arithmetic sequence.

Successive terms in a sequence are just what they sound like—the term that comes after the current one. When analyzing a sequence, successive terms play a crucial role as they help determine the type of sequence you are dealing with. If you're examining an arithmetic sequence, you look at the differences between successive terms. For a geometric sequence, you focus on the ratio between successive terms.

Observing successive terms helps to discern a pattern in the sequence. The exercise provided uses successive terms to establish whether the pattern represents an arithmetic or a geometric sequence. By looking at how each term relates to the one before it, it's possible to conclude the nature of the sequence.

A constant ratio in a sequence indicates that it's a geometric sequence, not arithmetic. This ratio is found by dividing a term by its predecessor. If the ratio is the same for all pairs of successive terms, that sequence is geometric. The exercise we're considering illustrates this concept: by dividing each term by the one before it (\(15 / 3\), \(75 / 15\), and \(375 / 75\)) and finding the constant ratio of 5, we identify the sequence as geometric.

A geometric sequence, thus, multiplies a fixed number (called the common ratio) to a term to get the next one. In other words, each term is the product of the previous term and the constant ratio, which in the given exercise is 5. This property is fundamental in understanding geometric progressions and is used to calculate terms further down the sequence.