A geometric sequence is a sequence where each term is found by multiplying the previous term by a constant value called the common ratio. It follows the general formula an = a1 * rn-1, where a1 is the first term and r is the common ratio.
The common ratio can be found by dividing any term in the sequence by the previous term. This will give you a constant value that is the common ratio for the entire sequence.
In an arithmetic sequence, each term is found by adding a constant value to the previous term. In a geometric sequence, each term is found by multiplying the previous term by a constant value. This means that in a geometric sequence, the terms increase or decrease at an exponential rate, while in an arithmetic sequence, the terms increase or decrease at a constant rate.
The formula for finding the nth term in a geometric sequence is an = a1 * rn-1. This formula can be used to find any term in the sequence by plugging in the value of n and solving for an.
Yes, a geometric sequence can have a negative common ratio. This means that the terms in the sequence will alternate between positive and negative values. For example, a geometric sequence with a common ratio of -2 would look like: 1, -2, 4, -8, 16, ...