Sum of Multiples of 3 from 1 to 100

Consider the integers from 1 to 100. What is the sum of all integers that are multiples of 3 within this range?

To find the sum, you can identify the multiples of 3, starting from 3 up to the largest multiple of 3 under 100, which is 99.

Recall that the formula for the sum of an arithmetic series is:

$S_n = \f\frac{n}{2}\times (a + l)$

where:

• $S_n$ is the sum of the series,
• $n$ is the number of terms,
• $a$ is the first term, and
• $l$ is the last term.