Is calculating how much money you have in a financial savings instrument involves an arithmetic series?
I think the answer is no.
An arithmetic series has a constant difference between the terms, like 2+4+6+8+10+...+100 for example.
Savings accounts have compound interest, so that would be a geometric series, since the ratio of successive terms is constant. For example, if you have an account with $1000, and the interest rate is 6% (or 0.5% per month), you would earn $5 the first month, then (1.005)*($5) the second month, then (1.005)^2*($5) the third month, and so on.