Students engage in exercises designed to identify the common ratios in geometric sequences. By analysing sequences where each term is a multiple of the previous term, they learn to determine the factor by which successive terms increase or decrease. This practice enhances their ability to recognise patterns and relationships within sequences, which is crucial for their mathematical development and for understanding phenomena that follow exponential growth or decay.

This series of questions deepens students’ knowledge of geometric sequences, focusing on the properties and behaviors that define these sequences. Students explore how these sequences are formed, how to calculate any term in the sequence, and the implications of different common ratios. Understanding geometric sequences prepares students for advanced topics in mathematics and sciences, such as compound interest calculations and population modeling.

Students apply their understanding of geometric sequences to real-world scenarios, such as calculating compounded interest rates, predicting population growth, or modeling the decay of radioactive materials. These practical exercises demonstrate the relevance of geometric sequences in fields like finance, biology, and physics, highlighting the importance of mathematics in analysing and predicting real-life phenomena.