Arithmetic Recursive Functions

How do we use the previous term to find the next term in a sequences? The formula that we use to do this is called a Recursive Formula! Lets look at the table below and construct a recursive formula based on this table.

The recursive formula for an arithmetic sequence is:

an = an-1 + d

So in our table we know that d is the common difference, 2. we can plug in this value to our equation to get the recursive equation for our sequence:

an = an-1 + 2

With this formula, we can find the 5th term in the sequence by knowing the 4th term in the sequence. For example

a5 = a4 + 2

a5 = 8 + 2

a5 = 10

So the value of our 5th term is 10. Let's find the 6th term:

a6 = a5 + 2

a6 = 10 + 2

a6 = 12

The value of the 6th term is 12.

So, we have to know the value of the previous term in order to use this equation.