Sequences and series
Connect the rule between terms to the value at any position.
Choose an available lesson and work at your own pace.
- Arithmetic sequencesFind the nth term of an arithmetic sequence, recover the first term and common difference, test membership and solve threshold questions with original visual practice.
- Arithmetic seriesDerive the arithmetic series formula by pairing terms, find unknown sums and term counts, and solve integer threshold problems with original worked practice.
- Geometric sequencesFind the nth term and common ratio of geometric sequences, handle negative and zero ratios, and solve membership and logarithmic threshold questions.
- Finite geometric seriesDerive and use the finite geometric series formula, including negative ratios, unknown term counts, sums between two indices and logarithmic thresholds.
- Sum to infinityUnderstand when a geometric series converges, find its sum to infinity, calculate signed remainders and error bounds, and convert recurring decimals with worked practice.
- Sigma notationRead and write sigma notation, count terms correctly, evaluate arithmetic and geometric sums with shifted bounds, and solve equations and infinite tails.
- Recurrence relationsGenerate sequences from recurrence relations, recover initial values and constants, handle nonlinear rules, and verify explicit formulas including two-step recurrences.
More in this chapter
Sequence behaviour and modelling lessons are being prepared.