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An arithmetic sequence is a list of numbers in which each term is obtained by adding a fixed number to the previous term. This fixed number is known as the 'common difference'. Understanding arithmetic sequences is fundamental in various branches of mathematics and its applications.

For instance, if we start with the number 6 and repeatedly subtract 2, we are forming an arithmetic sequence with a common difference of -2. Each term in the sequence is simply the previous term with 2 subtracted from it. So, beginning with 6, our sequence starts like this: 6, 4, 2, 0, and so on. In this example, each number is called a 'term' of the sequence, and we see the pattern that forms as we apply the common difference recurrently.

When working with sequences, the ability to calculate any term efficiently is crucial. There are typically two ways to find the terms of a sequence: explicitly and recursively. An explicit formula provides a way to calculate any term directly, based on its position in the sequence, often denoted as 'n'.

On the other hand, a recursive formula defines each term in relation to the one before it, with one or more initial terms given. For arithmetic sequences, the explicit formula is usually in the form of 'an = a1 + (n - 1)d, while a recursive formula takes the general form of 'a_n = a_n-1 + d', where 'd' is the common difference.

Recursive formulas are a way of defining sequences where the subsequent term is determined from the previous ones through a set rule. The most important part of a recursive formula is it requires a starting point, which is typically given by the problem. In the recursive sequence of the current exercise, the formula given is 'a_n = a_n-1 - 2', with the initial condition that 'a₀ = 6'.

The formula tells us to subtract 2 from the preceding term to obtain the next one. For calculating terms of a recursively defined sequence, it is important to follow the steps of the recursion, always referring to the previous term. This makes calculation straightforward but requires us to work step by step, unlike an explicit formula which can be used to compute any term directly.