Let f (n) = 20n – n^2 (n = 1, 2, 3 ..... ), then

Consider $f(x) = 20x – x^2$, defined for all real number x. $f’(x) = 20 – 2x$ and $f”(x) = – 2$.

Hence x = 10 is a point of maximum.

Thus the maximum value of f(n) is 200 – 100 = 100