In Exercises 63–64, find a2 and a3 for each geometric sequence.
2, a2, a3, - 54
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Geometric Sequence
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. For example, in the sequence 2, a2, a3, -54, the first term is 2, and the subsequent terms are generated by multiplying by the common ratio.
The common ratio in a geometric sequence is the factor by which we multiply each term to get the next term. It can be found by dividing any term by the preceding term. In the given sequence, once we determine a2 and a3, we can find the common ratio by using the relationship between these terms and the first term.
To find specific terms in a geometric sequence, we can use the formula for the nth term, which is given by a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio. By applying this formula, we can calculate a2 and a3 based on the known first term and the common ratio derived from the sequence.