About this topic
Before you begin
Find arithmetic and geometric terms and sums, interpret recurrence relations and justify convergence and integer thresholds.
Learning goals
- Calculate a specified arithmetic progression term
- Calculate a finite block of arithmetic progression terms
- Calculate a specified geometric progression term
- Calculate a finite block of geometric progression terms
- Determine a geometric series' finite sum or nonconvergence
- Find terms and blocks of terms from a partial-sum formula
- Sum a series formed from arithmetic and geometric parts
- Express and use the general term of a sequence
- Find finite sums and analyse convergence of series
- Calculate a specified term of an affine recurrence
- Determine an affine recurrence's finite limit or nonconvergence
Syllabus statements covered
- Include: finite and infinite sequences and series; sequence as y = f(n) for positive integer n; nth term u_n and sum S_n relationship; sequences defined by nth-term formula or u_(n+1) = f(u_n), including calculator or computer generation; sum and difference of two series; convergence and sum to infinity; nth term and finite sum of arithmetic and geometric series; condition for convergence and sum to infinity of an infinite geometric series.
- Include: finite and infinite sequences and series; sequence as y = f(n) for positive integer n; nth term u_n and sum S_n relationship; sequences defined by nth-term formula or u_(n+1) = f(u_n), including calculator or computer generation; sum and difference of two series; convergence and sum to infinity; nth term and finite sum of arithmetic and geometric series; condition for convergence and sum to infinity of an infinite geometric series.
Choose a lesson
Work through them in order.
- Not startedArithmetic, geometric and partial sumsNextDerive term and sum rules, retain geometric-ratio conditions, and check the first index and integer thresholds.
- Not startedRecurrence and convergenceNextGenerate valid terms, prove affine limits through their errors, and distinguish sequence, series and numerical stopping claims.