Question

1. what is the sum of the first 20 multiples of five?

\\(s_{20} = 1,550\\)

\\(s_{20} = 2,100\\)

\\(s_{20} = 1,000\\)

\\(s_{20} = 1,050\\)

Explanation:

🆕 New Concept Discovered: Arithmetic Series
Adding up the terms of an arithmetic sequence

Step 1: Identify the sequence

The first 20 multiples of five form an arithmetic sequence where each term increases by 5:

$$ a_1 = 5 $$

$$ d = 5 $$

$$ n = 20 $$

The last term (\(a_{20}\)) is:

$$ a_{20} = 20 \times 5 = 100 $$

Step 2: Apply the sum formula

To find the sum of an arithmetic series, we use the formula:

$$ S_n = \frac{n}{2}(a_1 + a_n) $$

Substitute the known values into the formula:

$$ S_{20} = \frac{20}{2}(5 + 100) $$

$$ S_{20} = 10(105) $$

$$ S_{20} = 1,050 $$

Answer:

\( S_{20} = 1,050 \)