Final answer:
To find the second term of a geometric sequence with a sum of 7,812 and a common ratio of 5, we used the sum formula for geometric sequences. The first term is calculated to be 0.125, and multiplying this by the common ratio gives the second term, which is 0.625.
Step-by-step explanation:
The sum of the first 6 terms of a geometric sequence is 7,812, and the common ratio is 5. To find the second term of the sequence, we can use the formula for the sum of a geometric sequence, which is Sn = a1 * (1 - rn) / (1 - r), where Sn is the sum of the first n terms, a1 is the first term, r is the common ratio, and n is the number of terms. In this case, n is 6 and r is 5. Plugging in the values, we get:
7,812 = a1 * (1 - 56) / (1 - 5)
Solving for a1, we find that the first term is 0.125. Since the second term is just the first term multiplied by the common ratio, the second term a2 is 0.125 * 5 = 0.625. Thus, the correct answer is a. 0.625.