Sequences and series. Game on.

The common difference is $14 - 20 = -6\textsf{.}$ From the sixth term to the ninth term there are $3$ steps, so the ninth term is $14 + (-6) \times 3 = -4\textsf{.}$

$a_5 = 3 + 4(4) = 3 + 16 = 19$.

Geometric series with $a_1 = 1$, $r = 2$, $n = 3$. Sum $= 1 + 2 + 4 = 7$.

The common ratio is $\dfrac{18}{6} = 3\textsf{.}$ From the third term to the sixth term there are $3$ steps, so the sixth term is $18 \times 3^{3} = 486\textsf{.}$

$a_4 = 2 + 3(5) = 2 + 15 = 17$.

Geometric series with $a_1 = 3$, $r = 2$, $n = 3$. Sum $= 3 + 6 + 12 = 21$.

The common ratio is $\dfrac{16}{8} = 2\textsf{.}$ From the fourth term to the seventh term there are $3$ steps, so the seventh term is $16 \times 2^{3} = 128\textsf{.}$

$a_{4} = 5 + 3(3) = 14$.