Iterative Notation and Geometric Sequences WORKSHEET
Suitable for Year groups: Year 10, Year 11
GCSE Tier: Higher
Targeting grades: 6-7
Prerequisite knowledge: Arithmetic including decimals, fractions, and directed numbers. Ability to describe and continue geometric sequences including finding the common ratio.
Iterative Notation and Geometric Sequences WORKSHEET DESCRIPTION
This worksheet develops students' understanding of geometric sequences through iterative notation.
Section A requires students to identify the next term, first term, common ratio, and express sequences using iterative notation. Students work with various sequences including positive/negative terms, fractions, and decimals, then use given iterative formulae to generate sequence terms.
The complexity increases in Section B as iterative formulae of the form xn+1 = a xn + b are introduced. These are not geometric sequences but rather mixed recursive relationships combining multiplication and addition.
This progression from simple geometric patterns to more complex iterative relationships helps students understand how sequences can be generated through recursive rules, building essential foundations for advanced sequence work and mathematical modelling.
