notation structure confusion

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I am new to writing notations and therefore I lack a little bit the experience on how to express something very simple. Basically, I want to describe the euclidean distance between two RGB colors. Each of the two colors, however was derived from taking the mean of a color swatch. I tried the following, but feel very illiterate:

I have to color swatches $\mathcal{S_1}$ and $\mathcal{S_2}$. Those color swatches in turn consist out of five RGB colors . $$\mathcal{S_1},\mathcal{S_1} = { c_{rgb_{1}} ... c_{rgb_{5}} }$$

Each RGB color consists of three values, which span from 0 to 255.

how would this be expressed for each of the rgb channels? $$ c_{rgb_{i}} = {v | v \text{is an integer, and} 0 \geq v \leq 255 }$$

To measure the distance between those two swatches, I took the mean of all each channel r,g,b in s1 and the same with s2 to create two new cumultive RGB values.

here I dont know how to express this

Finally, these resulting RGB colors, I then used to calculate the Euclidean distance with:

\begin{equation} dist = \sum_{i=1}^{n} \sqrt{(}(R_i^a - R_i^b)^2 + (B_i^a - B_i^b)^2 + (G_i^a - G_i^b)^2) \end{equation}

Thanks for the hints!