IB Math AI Worksheet 1.3 - Geometric Sequences

IB Math AI SL 1.3 – Geometric Sequences Worksheet

Topic: Number and Algebra
Level: IB Mathematics: Applications and Interpretation (SL)
File Type: Printable Worksheet / Student Practice Sheet

Overview

This worksheet provides comprehensive practice on geometric sequences and series, developing students’ understanding of multiplicative patterns and exponential change introduced in IB Math AI SL Topic 1.3.
Learners will identify geometric relationships, derive general terms, compute sums of finite and infinite series, and apply these ideas to real-world contexts such as growth and decay.

The worksheet complements the corresponding lesson slides and promotes procedural fluency through scaffolded examples, cumulative practice, and contextual applications.

Learning Objectives

By completing this worksheet, students will be able to —

• Determine whether a sequence is geometric and find its common ratio.
• Derive and apply the general term (U_n = a r^{,n-1}).
• Evaluate geometric series using the standard sum formula.
• Solve for an unknown number of terms in a geometric series.
• Apply geometric growth and decay models to practical problems, including population and finance scenarios.

What’s Included

• Exercises determining the common ratio and nth term of geometric sequences.
• Guided questions on using explicit formulas to find specific terms.
• Problems evaluating finite geometric series and finding unknown parameters.
• Real-world applications, including training schedules and bacterial growth.
• Step-by-step worked answers for independent study or class review.
• Clear, printable format suitable for individual practice or homework.

Topics Covered

• Definition and identification of geometric sequences.
• nth-term formula and explicit forms of geometric sequences.
• Sum of finite geometric series.
• Determining the number of terms in a series.
• Applications to exponential growth and decay contexts.

Why You’ll Love It

Perfectly aligned with IB Math AI SL Topic 1: Number and Algebra, this worksheet bridges abstract concepts and real-world applications. It builds students’ confidence in recognizing and modeling multiplicative patterns, making it ideal for classroom reinforcement, revision, or exam preparation.

Tags

IB Math AI SL, IB Mathematics, Number and Algebra, Geometric Sequences, Geometric Series, nth Term, Common Ratio, Exponential Growth, Exponential Decay, Sequences and Series, IB Math Worksheet, Printable Math Worksheet, Student Practice Sheet, IB Topic 1, Finite Geometric Series, Math Revision, IB Math Resources, Full Marks Education