recursive formula

Question

write a recursive formula for a(n) = -8n+7

Answer 1

If you write out the first few terms, you'll see

a(1)=-1

a(2)=-9

a(3)=-17

a(4)=-25

 

So you need to notice that each successive term goes down by 8, starting from -1.

 

So A(1)=-1

a(n) = a(n-1) -8

 

This is the recursive definition.

Answer 2

Tamara,

A recursive formula is written in terms of what you do to a term to get the next term. In other words, if the current term is 8, and the rule is +4, the next term is 12.  The simplest way to find the recursive formula is to make a table of values base on the equation, and look at the changes that occur.

  n      a(n)

  0      7

  1     -1

  2     -9

  3     -17

 

You can see that the a(n) values have a common difference of -8. So we can write the recursive formulas as:

 

a_n = a_n-1 - 8

 

You may notice that the -8 corresponds to the slope of the original equation. This will always be true for linear equations. It is not so clear cut for higher order functions. Hope this helps.

Bryan