18 Let $S(n)$ be the sum of the first $n$ positive integers, so $S(1) = 1$ and $S(2) = 1 + 2 = 3$.
a Find $S(3)$.
b $S(n)$ can be modelled by the quadratic function $S(n) = an^2 + bn + c$. Use technology
to find $a$, $b$, and $c$.
c Check that your model gives the correct result for the sum of the first 6 positive integers.
d Find the sum of the first 60 positive integers.
e Find $S(2\frac{1}{2})$. Is this result meaningful?
f For which values of $n$ is it appropriate to use this model?
