# Sequences and the Recursive rule

• March 6th 2008, 05:53 PM
blackrider76
Sequences and the Recursive rule
This problem has been driving me crazy:

Specify each sequence both explicitly and recursively. (Hint: For the recursive rule, consider a(subscript: n+1) - a(subscript: n)

1, 4, 9, 16, 25...

I need help on what they mean by a(subscript: n+1) - a(subscript: n). I know it has something to do with moving a(subscript: n) over in the recursive rule equation (a[subscript: n+1] = a[subscript: n] + D where D is the common difference) but I can't figure it out...
• March 6th 2008, 06:02 PM
TheEmptySet
Quote:

Originally Posted by blackrider76
This problem has been driving me crazy:

Specify each sequence both explicitly and recursively. (Hint: For the recursive rule, consider a(subscript: n+1) - a(subscript: n)

1, 4, 9, 16, 25...

I need help on what they mean by a(subscript: n+1) - a(subscript: n). I know it has something to do with moving a(subscript: n) over in the recursive rule equation (a[subscript: n+1] = a[subscript: n] + D where D is the common difference) but I can't figure it out...

The sequence is generated by

$a_n=n^2$ for n =1,2,3...

as far as adding a Common difference D that only works for arithmetic sequences and this isn't one.
• March 6th 2008, 06:04 PM
blackrider76
Just because there is no common difference does not mean you cannot specify the function recursively What you need is $a_{n+1} = a_n + f(n)$. You should be able to spot a pattern in the differences ( $a_{n+1}-a_n$)and express it in terms of n.