- #1

mr_coffee

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Hello everyone, I'm having some issues on a few problems and I'm not sure if i did the first one I'm going to post right, any help or clarifcation would be great.

The directions are: In eavch of 3-15 a sequence is defined recursively. Use iteration to guess an explicit formula for the sequence.

and here is my work:

http://img518.imageshack.us/img518/8013/scan0001pa5.jpg

For the last one, I see that the 2 is increasing at the same rate as the 3^k, but i have no idea about the pattern, I'm not sure what technique I'm suppose to use, i know they said "guess" a formula, but what will help me make an educated guess? Of course there are some easy ones like n! that i can recongize but these arn't so easy for me to see what's going on.

I can see i can factor out a 2 and a 3^2 from p_4 but i don't see how that is going to help me much, getting:

[tex]2^4 + 3^4 + 2*3^2(1 + 3)[/tex]

thanks!

The directions are: In eavch of 3-15 a sequence is defined recursively. Use iteration to guess an explicit formula for the sequence.

and here is my work:

http://img518.imageshack.us/img518/8013/scan0001pa5.jpg

For the last one, I see that the 2 is increasing at the same rate as the 3^k, but i have no idea about the pattern, I'm not sure what technique I'm suppose to use, i know they said "guess" a formula, but what will help me make an educated guess? Of course there are some easy ones like n! that i can recongize but these arn't so easy for me to see what's going on.

I can see i can factor out a 2 and a 3^2 from p_4 but i don't see how that is going to help me much, getting:

[tex]2^4 + 3^4 + 2*3^2(1 + 3)[/tex]

thanks!

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