In “aₙ = a₁ + (n-1)d,” why is there a “ₙ”?
The subscript n represents the “nth” term of an arithmetic sequence. You could also say that it is the “position” of the term in the sequence
as an example of aₙ=a₁(n-1)d, take the arithmetic sequence 1,4,7,10,13. Because these are going up by a constant of 3, d=3. Now the equation looks like aₙ=a₁(n-1)(3). Say the question asks for the 10th term in the sequence. Now, the equation would look like a10=1(10-1)(3). Once you solve, the answer would be a10=27.