Geometric sequences of numbers

A geometric sequence increase or decrease by a common factor - the common ratio.


Example

figure19

The common ratio is 2. We can write this as an algebraic expression.

an=a1rn1

Where an is the first number (in this case 2).

r is the common factor (in this case 2).

n is the place in the set the number has (2 has n = 1, 8 has n = 3 etc.

We can rewrite this formula for our specific sequence:

an=22n1

If we would like to know the next number in the sequence after 32. The next number in the sequence is the 6th number. This gives us:


Example

an=arn1

a6=2261

a6=225

a6=232

a6=64


Video lesson

Find the eighth number