Welcome to this deck on sequences. A sequence is simply a list of numbers that follow a rule. We'll explore three main types: linear, quadratic, and geometric. By the end, you'll be able to spot the pattern in each type and find the formula for the nth term, which lets you calculate any term in the sequence.

Let's start with the simplest type: linear sequences. These are also known as arithmetic sequences. In a linear sequence, you get from one term to the next by adding or subtracting the same number every time. For example, in the sequence 5, 8, 11, 14, we are adding 3 at each step.

The term-to-term rule is useful, but what if you wanted to find the 100th term? It would take a long time to add the difference 99 times. A much faster way is to find a formula called the nth term. This formula lets you find any term in the sequence, just by substituting the term number, 'n'.

For a linear sequence, the nth term formula always contains the common difference multiplied by 'n'. For example, if the common difference is 4, the nth term formula will start with '4n'.