Unit 9 · Core unit
Sequences and series alongside the model-selection judgement that closes the course.
What a strong answer looks like
A strong answer justifies the chosen model from the pattern of change and states whether a result is exact or approximate.
Know
Arithmetic sequences add a common difference; geometric ones multiply by a ratio. An infinite geometric series converges only when the ratio is below one in absolute value.
Apply
Identify the type from consecutive terms, then apply the matching formula.
Watch out
Applying an infinite sum formula to a divergent series.
Study move
Decide convergence for three series and sum those that converge.
Know
Constant differences suggest linear, constant second differences quadratic, and constant ratios exponential. The evidence, not the appearance, decides.
Apply
Compute differences and ratios before choosing.
Watch out
Choosing exponential merely because the values grow quickly.
Study move
Identify the family for three tables with stated evidence.
Know
A graphing tool answers questions algebra cannot reach exactly, but its answers are approximate and must be labelled so.
Apply
Use technology for intersections and regressions, and report the precision honestly.
Watch out
Presenting a rounded graphical result as an exact value.
Study move
Solve one problem exactly and one graphically, labelling each.
Modeling drill
A deposit is made annually into an account earning interest. Write the expression for the balance and say which sequence type it uses.
