An arithmetic series has first term 5 and common difference 3. Find the sum of the first 20 terms.

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A geometric series has first term 12 and common ratio $\frac{1}{3}$ . Find its sum to infinity.
A sequence is defined by $u_{n + 1} = 2 u_{n} - 1$ with $u_{1} = 3$ . Find $u_{4}$ .
A line passes through $(1, 3)$ with gradient $- 2$ . What is its equation?
Find the centre and radius of the circle $x^{2} + y^{2} - 6 x + 4 y - 12 = 0$ .
A line has equation $3 x + 2 y = 7$ . What is the gradient of a line perpendicular to it?
Points $A (1, 2)$ and $B (5, 5)$ are given. What is the length of $A B$ ?

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