Recursive Formulas & Sequences

• Apr 30th 2009, 06:39 PM
helpme
Recursive Formulas & Sequences
Directions tell me to provide a recursive formula for the sequence and to specify what type of sequence it is.

1] 1,1,2,3,5,8

2] 5,10, 20, 40, 80, 160

I understand the patterns & how they derived the terms, but I can't figure out how to write the recursive formula. Help, please & thank you.

• Apr 30th 2009, 06:41 PM
Prove It
Quote:

Originally Posted by helpme
Directions tell me to provide a recursive formula for the sequence and to specify what type of sequence it is.

1] 1,1,2,3,5,8

2] 5,10, 20, 40, 80, 160

I understand the patterns & how they derived the terms, but I can't figure out how to write the recursive formula. Help, please & thank you.

For 1) what is 1 + 1?

What is 1 + 2?

What is 2 + 3?

What is 3 + 5?

Can you see that each term is the sum of the two that preceded it?

So $f_{n + 2} = f_{n + 1} + f_n$

This is called the Fibonnaci Sequence.

Note: There is actually a term missing. It should be 0, 1, 1, 2, 3, 5, 8, ...

2) What is 5 x 2?

What is 10 x 2?

What is 20 x 2?

Can you see that each term is the previous term multiplied by 2?

So $f_{n + 1} = 2f{n}$.
• Apr 30th 2009, 07:03 PM
helpme
Quote:

Originally Posted by Prove It
For 1) what is 1 + 1?

What is 1 + 2?

What is 2 + 3?

What is 3 + 5?

Can you see that each term is the sum of the two that preceded it?

So $f_{n + 2} = f_{n + 1} + f_n$

This is called the Fibonnaci Sequence.

Note: There is actually a term missing. It should be 0, 1, 1, 2, 3, 5, 8, ...

2) What is 5 x 2?

What is 10 x 2?

What is 20 x 2?

Can you see that each term is the previous term multiplied by 2?

So $f_{n + 1} = 2f{n}$.

for number 2. it's a geometric sequence right?
& my common ratio is 2...
so I can write my formula as An = 2An-1 ?

thanks, btw.
• May 1st 2009, 12:17 AM
Prove It
Quote:

Originally Posted by helpme
for number 2. it's a geometric sequence right?
& my common ratio is 2...
so I can write my formula as An = 2An-1 ?

thanks, btw.

Yes it's a geometric sequence.

And yes, writing $A_n = 2A_{n - 1}$ is fine.