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
Stacey Warren - Expert brainly.com
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you have the rule, and the starting values ... just use them
If I knew how to do that I probably would have done that. I have no idea how to do this problem.
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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 ...
then let n=3, then 4, then 5
and you will generate the list of values with each new calculation
Oh, I see. I have to write out each one
it would help yes .... the process is short enough that it is the most efficient method
if youhad to find say a103 then finding a closed form would be more suitable
or writing a computer code to work it thru for you :)
I still do not think I am doing this correctly. My answer is x+2x^2+5x^3+13x^4+34x^5
a_(2) = 3 a_(1) - a_(0)
but a_(0) = 1 and a_(1) = 1
so, a_(2) = 3(1) - 1 = 2
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 ...