What the learner will study

• Arithmetic Sequences: Explicit & Recursive Forms
• Geometric Sequences: Growth, Decay & Recursion
• General Sequences, Patterns & Difference Tables
• Finite Arithmetic & Geometric Series
• Infinite Geometric Series & Convergence
• Sigma Notation & Summation Properties
• Pascal’s Triangle & the Binomial Theorem

How to support without taking over

• Ask the learner to define inputs, outputs, units, and domain.
• Ask which property or theorem justifies each transformation.
• Request an independent check by substitution, graph, table, or alternate method.
• Encourage correction notes rather than erasing evidence of learning.
• Use the calculator after the mathematical setup is visible.

Evidence to preserve

Keep one worked example, one correction, one application or project artifact, the mastery result, and a reflection explaining growth and next steps.

Applied investigation

Sequence, Series & Repeated-Change Analysis asks the learner to define a real question, construct mathematics, validate results, state uncertainty, and communicate a defensible conclusion.