anonymous
  • anonymous
Let A(x)= SUM(a_nX^n) be the generating function of the sequence a_0, a_1, a_2, ... that is recursively defined by a_0=a_1=1 and a_n=3(a_(n-1))-(a_(n-2) where (n>=2). Compute a_5
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
amistre64
  • amistre64
you have the rule, and the starting values ... just use them
anonymous
  • anonymous
If I knew how to do that I probably would have done that. I have no idea how to do this problem.
amistre64
  • amistre64
let n=2, what does the rule become?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

amistre64
  • amistre64
a_n = 3 a_(n-1) - a_(n-2) 2 2 2 a_2 = 3 a_(2-1) - a_(2-2) a_2 = 3 a_(1) - a_(0) and we have the values for 0 and 1 already stated ...
amistre64
  • amistre64
then let n=3, then 4, then 5 and you will generate the list of values with each new calculation
anonymous
  • anonymous
Oh, I see. I have to write out each one
amistre64
  • amistre64
it would help yes .... the process is short enough that it is the most efficient method
amistre64
  • amistre64
if youhad to find say a103 then finding a closed form would be more suitable
amistre64
  • amistre64
or writing a computer code to work it thru for you :)
anonymous
  • anonymous
I still do not think I am doing this correctly. My answer is x+2x^2+5x^3+13x^4+34x^5
amistre64
  • amistre64
a_(2) = 3 a_(1) - a_(0) but a_(0) = 1 and a_(1) = 1 so, a_(2) = 3(1) - 1 = 2
amistre64
  • amistre64
lets forgo the _(n) stuff becuase its a bugger to type a3 = 3 a2 - a1, but we know a2 and a1 a3 = 3(2) - 1 = 5 -------------------- a4 = 3 a3 - a2, but we know a3 and a2 a4 = 3(5) - 2 = 13 --------------------- a5 = 3 a4 - a3, but we know a4 and a3 ...
anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
Does that mean my generating function is correct?

Looking for something else?

Not the answer you are looking for? Search for more explanations.