Final answer:
Using the formula for the sum of an arithmetic sequence, the sum of the first 20 terms with a first term of 3 and a common difference of 8 is calculated to be 1580. However, this result does not match any of the provided options, suggesting a possible error in the question or options presented.
Step-by-step explanation:
To determine the sum of the first 20 terms of an arithmetic sequence with a first term a_1 = 3 and a common difference of d = 8, we can use the formula for the sum of the first n terms of an arithmetic sequence:
S_n = \frac{n}{2}(2a_1 + (n - 1)d)
In this case, the sum of the first 20 terms is:
S_{20} = \frac{20}{2}(2 × 3 + (20 - 1) × 8)
Calculating this gives us:
S_{20} = 10(6 + 19 × 8) = 10(6 + 152) = 10(158) = 1580
However, none of the provided options matches the calculated sum of 1580. Thus, it seems there might be an error within the question or the options provided. Please double-check the question or the options for any discrepancies.