Finding The Next Term Of A Sequence — Interactive Lesson (KS3)

This Nth Term of a Linear Sequence lesson teaches students to generate terms in a sequence from a given formula, and to work out the formula for the nth term of a linear sequence themselves. Across 17 slides, a worked example walks through the sequence generated by 3n − 1, showing how the terms 2, 5, 8, 11 and 14 are produced, before students apply the same method to new sequences.

The lesson explains the key idea clearly: the common difference between terms (here, the sequence goes up in 3) appears as the coefficient of n in the formula, giving students a reliable method rather than relying on guesswork.

By the end of the lesson, students will be able to generate terms in a sequence using a given formula, and find the formula for the nth term of a linear sequence — two closely linked KS3 algebra skills that build directly into later work on quadratic and other non-linear sequences.

This builds directly on earlier work describing sequences in words, moving students towards the more formal algebraic notation they will need for quadratic and other non-linear sequences later in the course.

The lesson is interactive and self-marking throughout, with instant feedback on every question, so it works equally well for whole-class teaching, independent practice or homework.