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?n^th?term?of a linear sequence in terms of n
• This formula will be in the form:n^th?term = dn + bwhered is the common difference, b is a constant that makes the first term “work”

How to find the n^th?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