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.