KS4. Algebra & Graphs. Finding the nth term of sequences

We have already looked at sequences earlier in the year. Now we want to focus more carefully on how to find the nth term of different sequences. The nth term is a rule that let’s us calculate the value of a specific term of the sequence, given its position in the sequence (e.g. the 213th term in the sequence).

Linear sequences

A linear sequence (also known as an arithmetic sequence) is one where each term in the sequence is a fixed amount larger than the previous term. eg. 10, 13, 16, 19, 22, … is a linear sequence.

For this kind of sequence we can use a special technique to calculate the nth term of the sequence.

This technique is illustrated below:

Let’s try this together for a few sequences from the following:

Linear Sequences Exercise

Answers

Quadratic Sequences

Finding the nth term with quadratic sequences follows a similar process.

In this case, if we identify that the “second difference” between the terms of the sequence is quadratic, then we know it must be a quadratic sequence with the form $an^2 + bn + c$ , so our job is to use the first, second and third term to identify the coefficients a, b and c for our specific sequence.