"How do I write a loop which creates a random number and adds the previous values?"
To add to the previous value, the loop must start at index #2. See inline comments for details.
n = 23;
a = [randn(1), nan(1,n-1)];
for i = 2:n;
a(i) = a(i-1) + randn(1);
However, you don't need a loop. This line does the same thing as the loop above.