A sequence $u_1,\ u_2,\ u_3,\ ...$ satisfies $u_{n+1}=Au_n+B$ where $A$ and $B$ are non zero constants. The second and third term of this sequence are 464 and 428, respectively. Given further that the sequence converges to $320$, find the value of the fourth term of this sequence.
$401$
An arithmetic progression has first term 11. The sum of its first 20 terms is 1360, and the sum of its last 20 terms is 4720. Determine the number of terms in the progression.
$48$
Find the equation of the tangent to $y=(3-x)^{\frac{3}{2}}$ when $x=1$.
$y = -\dfrac{3\sqrt{2}}{2}x + \dfrac{7\sqrt{2}}{2}$
Use proof by contradiction to prove that $\log_23$ is irrational.
Standard proof by contradiction using $\log_2 3 = \dfrac{p}{q} \Rightarrow 2^p = 3^q$