Find the nth term of the quadratic sequence 2, 9, 20, 35, ...

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Solve the simultaneous equations: $y = 2 x - 3$ and $x^{2} + y^{2} = 18$ .
Find the $n^{th}$ term formula for the quadratic sequence: $5, 11, 19, 29, 41, \dots$
Simplify the algebraic fraction fully: $\frac{2 x ^{2} - 7 x - 4}{4 x ^{2} - 1}$ .
Write $2 x^{2} + 12 x + 11$ in the completed square form $a (x + b)^{2} + c$ .
Solve the inequality: $x^{2} - 4 x - 12 > 0$ .
The functions $f$ and $g$ are defined as $f (x) = \frac{2 x + 3}{x - 1}$ ( $x \neq = 1$ ) and $g (x) = x^{2} - 5$ . Solve the equation $f^{- 1} (x) = 4$ …