Introduction
Summing the terms of a progression is one of the most frequently examined skills in the 9709 Paper 1 series topic. Whilst the prerequisite work on arithmetic and geometric progressions (APs and GPs) establishes the structure of each sequence, this subtopic focuses on applying the sum formulae — often alongside the nth-term formulae — to solve multi-step problems. Examiners regularly combine both types in a single question, require you to form and solve simultaneous equations, or embed the formulae inside inequalities. Mastery here directly rewards marks.
Core Concept
An arithmetic progression has a constant difference between consecutive terms; a geometric progression has a constant ratio between consecutive terms. Once you know the first term and the common difference or ratio, you can find:
- any individual term using the nth-term formula, and
- the total of the first terms using the sum formula.
The key exam skill is translating a word problem or algebraic condition into one or two equations involving these formulae, then solving for the unknown quantities.
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