Originally Posted by

**scotchegg** I recently was given a very old Scottish Qualifications Higher paper from 1987. I could do almost every question easily, but when it came to question 10, I was entirely stumped. I have never been taught how to do it (and therefore don't really know what the problem is called so to speak), but here it is anyway. I would be happy if you could shed some light on this.

10. The sum Sn of the first n terms of an arithmetic series is given by

$\displaystyle S_n = 4n - n^2$

a) Find i) $\displaystyle u_1$ and $\displaystyle u_2$, the first 2 terms

ii) the common difference

b) Calculate the sum of the first 50 terms of the series

$\displaystyle u_1 + u_3 + u_5 + \ldots $