What is the missing values in the function table?

Question

In: 0, 1, 2, 3, 4, 5...895

 

Output: -3, -1, 1, 3, 5, ?, ?

Answer 1

IN   OUT  1st Difference

 0    -3    

 1    -1      2

 2     1      2

 3     3      2

 4     5      2

 5     ?   

 ...

895  ?

 

Since the first difference is a constant (2), the function is linear and the recursive equation is f(n) = f(n-1) + 2.  Hence f(5) = f(4) + 2 = 5 + 2 = 7.  To find f(895), use the explicit form of the linear equation, f(x) = 2x - 3.  f(895) = 2*(895) - 3 = 1792.