Final answer:
To find the first term of a geometric series with a given sum, common ratio, and number of terms, we use the sum formula for a geometric series. By substituting the given values into the formula and solving for the first term, we find the first term is approximately 640.96, which corresponds to answer choice A.
Step-by-step explanation:
The question asks to find the first term, a₁, of a geometric series. To solve this, we can use the formula for the sum of a geometric series, which is Sn = a₁ * (1 - r^n) / (1 - r), where Sn is the sum of the series, a₁ is the first term, r is the common ratio, and n is the number of terms. Given that Sn is 48,785, r is 3.4, and n is 3, we can rearrange the formula to solve for a₁.
Firstly, let's plug the values into the formula:
48,785 = a₁ * (1 - 3.4^3) / (1 - 3.4)
Calculating the right side of the equation:
48,785 = a₁ * (1 - 39.304) / (1 - 3.4)
48,785 = a₁ * (-38.304) / (-2.4)
48,785 = a₁ * 15.96
Now, divide both sides by 15.96 to find a₁:
a₁ = 48,785 / 15.96
a₁ ≈ 3056.89 / 15.96
a₁ ≈ 640.96
Therefore, the correct answer is A) 640.96.