any way to avoid this loop?

I'm familiar with the benefits of vectorizing code, but is there a way to avoid a loop when the solution to each value in an array depends on the value before it? A minimal working example of a loop I'd like to avoid:

x = ones(1,1000); 

for n = 2:length(x)
    x(n) = 2*x(n-1) - 10;
end

Ideas for a generalized solution? Or perhaps there's simply a faster technique I should learn about?

Answer 1

[per isakson]

See: 1-D digital filter

[Chad Greene]

Brilliant! Exactly the solution I was hoping for. Thank you!