Unit 5 · Core unit
Patterns with a rule, and the sums they generate. The distinction between an explicit and a recursive rule runs through the whole unit.
What a strong answer looks like
A strong answer names the sequence type from how consecutive terms relate, before applying any formula.
Know
Arithmetic sequences add a common difference; geometric sequences multiply by a common ratio. Checking both differences and ratios identifies which.
Apply
Test consecutive differences and ratios, then apply the matching explicit rule.
Watch out
Applying an arithmetic formula to a geometric sequence because the terms increase steadily.
Study move
Identify the type of three sequences before computing any term.
Know
An explicit rule computes any term directly; a recursive rule builds each from the previous, so it needs a starting value.
Apply
Convert between the forms, using the equilibrium value for recursions with a constant term.
Watch out
Omitting the initial term from a recursive definition, which leaves it undefined.
Study move
Convert one recursion into an explicit rule and verify at two terms.
Know
A finite series sums a fixed count of terms. An infinite geometric series converges only when the ratio is below one in absolute value.
Apply
Check the ratio before applying an infinite sum formula.
Watch out
Applying the infinite sum formula to a divergent series.
Study move
Decide convergence for three infinite series and sum the ones that converge.
Modeling drill
A theatre gains a fixed number of seats per row. Find the total seats and say which sequence type the row counts form.
