what real world suituations are used for arthimetic and geometric series and sequences?

Answer 1

Engineers use such sequences a lot in calculations of math models of physical things. However, we seldom apply all the rigor.

An infinite series is normally rounded off with a few terms, rather than proving the exacty solution.

Another example is in calculators. Computing e^x, for example, relies on the Taylor series approximation - the calculator actually carries out the first several terms.

Answer 2

1) population growth
2) interest rate calculations