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The common ratio in a geometric sequence is a steady value that every term is multiplied by to get the next term. It is represented as 'r' and must be a fixed, non-zero number. The common ratio plays a pivotal role in the sequence's behavior: if 'r' is greater than one, the sequence increases; if it's between zero and one, the sequence decreases; if 'r' is negative, the sequence alternates signs.

To determine the common ratio, divide any term in the sequence by the term before it (excluding the first term, which cannot be divided by the previous term since there isn't one). In our exercise example, dividing the second term by the first term \( -0.007 / 0.0007 = -10 \) resulted in the common ratio of -10, which indicates that every following term is 10 times the previous one and switches in sign because of the negativity of the ratio.

The general term of a geometric sequence, often denoted as \(a_n\), is the nth term and can be calculated using the formula: \[ a_{n} = a_{1} \cdot r^{n-1} \] where \(a_{1}\) is the first term of the sequence, \(r\) is the common ratio, and \(n\) is the term number. This formula lets you find any term in the sequence without listing all prior terms—a significant advantage when dealing with large sequences.

In our exercise, substituting the first term (\(0.0007\)) and the common ratio we found earlier (-10) into the formula, we can express the general term of this geometric sequence as: \[ a_{n} = 0.0007 \cdot (-10)^{n-1} \] This general formula is the backbone to finding any term in the sequence efficiently.

In mathematics, a sequence is an ordered list of numbers following some rule, while a series is the sum of the elements of a sequence. Sequences can be arithmetic, where each term is the previous term plus a constant difference, or geometric, like in the given exercise, where each term is the previous term multiplied by a constant ratio 'r'.

Understanding both sequences and series is fundamental for handling various mathematical and real-life problems. Sequences describe the pattern of individual events or measurements, while series are often used in finance for compound interest problems or in physics for calculating distances over time during constant acceleration.

Geometric sequences, with their exponential growth or decay, can model many natural and technological phenomena. Learning how to navigate through the concepts of common ratio, general term derivation, and the differences between sequence and a series, provides crucial tools for solving a wide range of practical problems.