diff --git a/lib/fibonacci.rb b/lib/fibonacci.rb
index 606755b..ec05b4a 100644
--- a/lib/fibonacci.rb
+++ b/lib/fibonacci.rb
@@ -5,8 +5,19 @@
 # ....
 # e.g. 6th fibonacci number is 8
 
-# Time complexity: ?
-# Space complexity: ?
+# Time complexity: O(n) - linear, because the number of loops is determined by the value of the input integer, "n."
+# Space complexity: Constant, because the algorithm only ever tracks 2 values, regardless of
+# the input integer.
 def fibonacci(n)
-  raise NotImplementedError
+  if n == nil || n < 0
+    raise ArgumentError, "The fibonacci number does not exist for #{n}"
+  else
+    fib = 0
+    x = 1
+    n.times do
+      fib += x
+      x = (fib - x)
+    end
+    return fib
+  end
 end