Question

Determine the sum of the first 20 terms, given that a,=3 and the common difference is 8?

Option 1: 620
Option 2: 520
Option 3: 720
Option 4: 820

Answer 1

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.