 #### Revision Notes

##### 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

where

• 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

1. Find the common difference between the terms – this is d.
2. Put the first term and n=1 into the formula, then solve to find b.

#### Example #### Question #### Answer ## Want to aim for a Level 9?

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