Sequences & Series: Arithmetic, Geometric & Their Money Uses

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Model a salary with a fixed yearly raise, add up ten years of pay two ways and find the year a salary goal is reached.
• Grow a subscriber list by a fixed percentage, depreciate a van, recover a growth rate from two counts and solve for a year with LN.
• Grow each yearly deposit to the end of the plan, add them up, and get the same total with the geometric series formula and with FV.
• Value payments that last forever, watch partial sums close in on that value, add up the path of a bouncing ball and value a growing perpetuity.
• Build the Fibonacci sequence and its golden-ratio limit, then model a fish population that grows and is fished every year.
• Turn Σ sums into one-cell formulas: a 12-month savings ladder, a can pyramid and sum-of-the-years'-digits depreciation.
• Compare a fixed-dollar raise with a percentage raise over 10 years, find the crossover year and chart both paths.
• Compute 20 partial sums of the harmonic series and of Σ 1/k², run a ratio test and chart the partial sums to see which series settles.