$12, 16, 20, \ldots$

$3, 1, -1, \ldots$

$a_n = 3n + 5$

$a_{n+1} = 4a_n - 7$ and $a_1 = 3$

$a_n = (n-3)(n+1)$

$a_1 = -1$, $a_{n+1} = \dfrac{3}{a_n + 2}$

$a_n = 8 - \dfrac{20}{3+n}$

$a_1 = 1$, $a_{n+1} = (3a_n + 2)^2$

$a_n = (-2n)^2$

$a_n = (-1)^n 7n^2$

$1, 4, 9, \ldots$

$1, 1+2, 1+2+3, \ldots$

$a_1b_1, a_2b_2, a_3b_3, \ldots$

$x, 2x^2, 3x^3, \ldots$

$a_1, a_1+d, a_1+2d, \ldots$

$a_1, a_1r, a_1r^2, \ldots$

$\dfrac{a_1}{b_1+c_1}, \dfrac{2a_2}{b_2+c_2}, \dfrac{3a_3}{b_3+c_3}, \ldots$

$\dfrac{1}{a_1}, \dfrac{1}{a_1+d}, \dfrac{1}{a_1+2d}, \ldots$