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Sequence terms, finite sums and finite-limit decisions topic check

Practise sequence terms, finite sums and finite-limit decisions in H2 Mathematics, check independently, and return later to review. This check covers selected skills, not the whole course topic.

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
Calculate a specified term of an affine recurrence
Determine an affine recurrence's finite limit or nonconvergence

GCE A-Level H2 Mathematics 2027

Revision notes

Revise sequences and series

Find arithmetic and geometric terms and sums, interpret recurrence relations and justify convergence and integer thresholds.

Key ideas

Arithmetic, geometric and partial sums
Derive term and sum rules, retain geometric-ratio conditions, and check the first index and integer thresholds.
Recurrence and convergence
Generate valid terms, prove affine limits through their errors, and distinguish sequence, series and numerical stopping claims.

What the syllabus asks

From the GCE A-Level H2 Mathematics 2027 syllabus

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.