(a) The sum of the first n terms of a sequence is given by \(S_{n} = \frac{5n^{2}}{2} + \frac{5n}{2}\). Write down the first four terms of the sequence and ...

(a) The sum of the first n  terms of a sequence is given by \(S_{n} = \frac{5n^{2}}{2} + \frac{5n}{2}\). Write down the first four terms of the sequence and an expression for the nth term.

(b) The equation of a circle is given by \(x^{2} + y^{2} - 10x - 8y + 25 = 0\).

(i) Show that the circle touches the x- axis ; (ii) Find the coordinates of the point of contact.