Arithmetic and Geometric Sequences – MYP Year 5 Extended

MYP Year 5 Extended: arithmetic and geometric sequences, nth term, sum formulas, and real-world modelling. Aligned to Criterion A and D.

Practice

Practice
Arithmetic & Geometric Sequences
180 min100 marks
Start Test
✦
Want help mastering this topic?
Work 1-on-1 with an IB expert tutor.
Book a session →

Overview

Arithmetic and geometric sequences are two of the most important sequence families in MYP Year 5 Extended algebra. Students need to be able to identify each type, apply the relevant formulas, and interpret both in real-world contexts.

Arithmetic Sequences

Key Features

An arithmetic sequence has a constant difference (d) between consecutive terms. The nth term formula is: uₙ = u₁ + (n − 1)d. Students must be able to find u₁ and d from any two terms, and calculate the sum of the first n terms using Sₙ = n/2 × (2u₁ + (n − 1)d).

Contextual Use

Arithmetic sequences appear in questions about constant growth — salary increases by a fixed amount each year, tiles added in a constant pattern, steps on a staircase. Recognising arithmetic behaviour in a context is just as important as applying the formula.

Geometric Sequences

Key Features

A geometric sequence has a constant ratio (r) between consecutive terms. The nth term formula is: uₙ = u₁ × r^(n−1). Students also work with the sum of n terms: Sₙ = u₁(rⁿ − 1)/(r − 1) for r ≠ 1.

Contextual Use

Geometric sequences appear in compound growth and decay contexts — population growth, depreciation, repeated percentage change. Students should be comfortable identifying when a context implies multiplicative (not additive) change.

Comparing the Two Types

A common Year 5 task asks students to compare an arithmetic and a geometric sequence with the same first two terms and determine which grows faster, or which better models a given situation. This requires both calculation and written justification.

MYP Assessment Relevance

Criterion A questions test formula application and calculation accuracy. Criterion D questions require students to model real-world scenarios using the correct sequence type and interpret their answer in context. Full marks on Criterion D require a written conclusion in plain language.

Common Mistakes

Frequently asked questions

You work with both arithmetic progressions (AP) and geometric progressions (GP): identifying the first term, common difference or common ratio, and using the nth term formulas a + (n-1)d and ar^(n-1). Also covers sum formulas Sn for AP and GP, including infinite GP sums where |r| < 1. Applications include compound interest, population growth, and salary increments. Sits as the core technical topic of Extended Unit 2.
Before reaching for a formula, check the relationship between consecutive terms. If you subtract pairs and get the same number, it's arithmetic; if you divide pairs and get the same ratio, it's geometric. A common mistake is assuming a sequence is arithmetic just because the numbers grow steadily. For GP sum questions, check whether r is greater than 1 or between 0 and 1 before deciding which form of Sn = a(r^n - 1)/(r - 1) to use.
Ready to start?
Book a free diagnostic.
Get started →

Related