What is a sequence?
- A sequence is simply a set of numbers (or objects) in an order
What is a linear sequence?
- A linear sequence is one where the numbers go up (or down) by the same amount each time
- eg 1, 4, 7, 10, 13, … (add 3 to get the next term)
- 15, 10, 5, 0, -5, … (subtract 5 to get the next term)
- If we look at the differences between the terms, we see that they are constant
What can we do with linear sequences?
- You should be able to recognise and continue a linear sequence
- You should also be able to find a formula for the nth term of a linear sequence in terms of n
- This formula will be in the form:
nth term = dn + b
d is the common difference, b is a constant that makes the first term “work”
How to find the nth term formula for a linear sequence
- Find the common difference between the terms – this is d
- Put the first term and n=1 into the formula, then solve to find b