How would you write incremental power of tens in mathematical terms

Question

I love mathematics but I have not done much beyond trigonometry. I would like to know

• (1) how to write this sequence as a formula $10^1, 10^2, 10^3, \ldots$ — assuming that can be written as a formula
• (2) what category of mathematics teaches the complex looking (eg: Greek characters) so I can learn more complex mathematics myself

Thanks!

PS. To clarify what I'm looking for I'm working on a multiplication scenario where numbers are implemented with linked lists per digit position. Implementing the above is easy for me. But I would like to truly understand in common mathematical terms what I'm doing. It looks something like this:

482 * 38 =

               /     16   * 10⁰
     ones (8) <|    64    * 10¹
               \   32     * 10²
               /     6    * 10¹
     tens (3) <|   24     * 10²
               \  12      * 10³
                 +
                 -------
                  18316

In a linked list scenario I don't need to increment the power per segment as above — it gets simplified to ones being shifted by power of zero, hundreds by power of one, etc (since the position of the addition in the linked list gets handed to the next linked list item from one loop that indexes the second multiplied number (eg: 38) which is used for the formula I've asked about).

Answer 1

$a_n = 10^n, n \in \{1, 2, \ldots\}$