# Thread: Sequences and the Recursive rule

1. ## 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...

2. 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

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

as far as adding a Common difference D that only works for arithmetic sequences and this isn't one.

Well, thanks. Now I won't waste even more time on this. <_<

4. Blackrider, I think you have got the wrong impression from TheEmptySet's completely correct post.
Just because there is no common difference does not mean you cannot specify the function recursively What you need is $\displaystyle a_{n+1} = a_n + f(n)$. You should be able to spot a pattern in the differences ($\displaystyle a_{n+1}-a_n$)and express it in terms of n.
4-1 = 3, for n = 1
9-4 = 5 for n = 2
16 -9 =7 for n = 3.
etc