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I have a question regarding on how to determine the impulse response of an LTI system which has the following conditions:

1).its input is x(n) = u(n) and output is y(n) = (1/2)

^{n}u(n) ,and

2).x(-1) = -1/3; x(0) = 1; x(1) = 1/2, and x(n) = 0 for all other values of n

My approach:

I know that x(n) can be expressed in terms of the sum from k=-infinity to k=+infinity of x(k)delta(n-k), so:

x(n) = x(-1)delta(n+1) + x(0)delta(n) + x(1)delta(n-1/2) ---> up to here am I right?

then,

I also know that the u(n) in y(n) = (1/2)

^{n}u(n) emphasized that h(n)= 0 for n<0

But after that I don't even know how to start in computing the impulse response h(n). I'm so lost here. can anyone help me with this? thank you soooo much.