# Geometric sequences of numbers

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

**Example**

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

$$a_{n}=a_{1}\cdot r^{n-1}$$

Where a_{n} 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:

$$a_{n}=2\cdot 2^{n-1}$$

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

**Example**

$$a_{n}=a\cdot r^{n-1}$$

$$a_{6}=2\cdot 2^{6-1}$$

$$a_{6}=2\cdot 2^{5}$$

$$a_{6}=2\cdot 32$$

$$a_{6}=64$$

**Video lesson**

Find the eighth number