Final answer:
The first term in a geometric sequence where the first term is "a" and each term is the product of the previous term and "r," is simply "a." This is because no multiplication by the common ratio "r" has occurred at the beginning of the sequence. The correct answer is A.
Step-by-step explanation:
In a geometric sequence, if the first term is "a" and each term is the product of the previous term and "r," the first term of the sequence would simply be "a." This is because the definition of the first term is that it is the starting point of the sequence, before any multipliers (in this case, "r") have been applied. So, the answer to the question is A) a.
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant called the ratio ("r").
The formula for the nth term of a geometric sequence is given by an = a * r(n-1), where "a" is the first term, "r" is the common ratio, and "n" is the term number. Thus, when calculating the first term (n=1), the formula simplifies to a * r0 = a, ensuring that the first term remains as "a."