Identify the Series

The first 25 multiples of 3 form an arithmetic progression (AP) where the first term $a = 3$, common difference $d = 3$, and number of terms $n = 25$.

$3, 6, 9, \dots, 3 \times 25 = 75$

Apply AP Sum Formula

The sum of an AP is given by $S_n = \frac{n}{2}(a + l)$, where $l$ is the last term ($75$).

$S_{25} = \frac{25}{2}(3 + 75) = \frac{25 \times 78}{2} = 975$

Calculate the Average

Average is calculated by dividing the total sum by the number of terms ($25$).

$\text{Average} = \frac{975}{25} = 39$

Direct Formula Verification

Using the shortcut formula for the average of the first $n$ multiples of $k$: $\frac{k(n+1)}{2}$.

$\text{Average} = \frac{3 \times (25 + 1)}{2} = \frac{3 \times 26}{2} = 39$