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A geometric progression is defined by a sequence of numbers where each term after the first is obtained by multiplying the previous term by a constant known as the common ratio. In this particular case, the first term of the progression is given as 3, while the second term is specified as -6. To determine the common ratio, one must divide the second term by the first term, which provides insight into the multiplicative relationship between these two consecutive terms.
By applying the formula for the common ratio, we take the second term, -6, and divide it by the first term, 3. This calculation yields a result of -2. Therefore, the common ratio of this geometric progression can be expressed as -2, indicating that each term in the sequence is derived by multiplying the preceding term by this value. This negative ratio suggests that the terms of the progression will alternate in sign, leading to a sequence that oscillates between positive and negative values.
Understanding the implications of the common ratio is crucial for analysing the behaviour of the geometric progression. With a common ratio of -2, the subsequent terms can be predicted with certainty. The third term would be calculated by multiplying the second term, -6, by -2, resulting in a value of 12. This pattern continues, demonstrating the exponential nature of geometric progressions, where each term is a product of the previous term and the common ratio, thereby creating a sequence that grows or shrinks in magnitude while alternating in sign.
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