Geometric Sequences | I Do, We Do, You Do | Year 10 Maths Foundation | Print Free

Help pupils understand how geometric sequences grow and shrink, use powers to calculate terms and explain whether a value can occur. This editable Year 10 Maths Foundation PowerPoint brings modelling, mini-whiteboard checks and substantial practice together in one print-free lesson. Keep the whole class working without photocopies.

BUILD CONFIDENCE WITH POWERS AND POSITIONS
The lesson connects a constant multiplier to simple position-to-term rules such as 2ⁿ, 3ⁿ and 0.5ⁿ. Pupils distinguish arithmetic from geometric sequences, identify common ratios and recognise powers. Increasing and decreasing examples help them see that multiplication does not always make a number larger.

WHAT IS INCLUDED
• One editable 68-slide PowerPoint with answers.
• Six retrieval questions and six prerequisite checks, each with grouped answers.
• Key vocabulary with numerical examples.
• A compact I Do / We Do page with three matched pairs and space for teacher working.
• Paired modelling solutions and an additional worked example on finding a term’s position.
• Twenty individual AFL questions, each immediately followed by its answer.
• A 36-question practice page organised into identifying nth-term rules, calculating terms and finding positions.
• One-page answers for the full practice set.
• Twenty-one differentiated questions across Developing, Secure and Greater Depth, plus one Super Challenge on the same slide.
• One-page differentiated answers and a separate worked challenge explanation.
• Two dedicated misconception checks with corrections.
• An original seven-mark exam-style question with worked answers.
• Three exit questions, each followed by its answer.

PROGRESSION THROUGH DIFFERENT DECISIONS
Practice moves beyond finding the next number. Pupils work backwards from a term value, check whether a value is skipped and locate the first term above or below a threshold. The differentiated tasks include recovering an earlier term, comparing powers and testing a claim about adding corresponding terms from two geometric sequences. Pupils explain using the common ratio.

A SUPER CHALLENGE BUILT ON REASONING
Two sequences double from different starting values. Can they ever share a term, even at different positions? Pupils must justify an answer that works however far the sequences continue. The worked solution uses the relationship between consecutive terms, so the challenge rewards explanation rather than a long list of calculations.

PRINT FREE AND READY TO TEACH
All differentiated levels and the challenge remain visible together. Short AFL prompts suit mini whiteboards, while the practice pages support exercise-book work. The Foundation focus is simple positive-ratio sequences and powers of positive rational numbers. Deriving the general geometric nth-term formula is not required.