1; 3; 9; 27;... Which statement best describes the pattern?

$1; 3; 9; 27; ...$

Divide the second term by the first: $\frac{3}{1} = 3$.
Divide the third term by the second: $\frac{9}{3} = 3$.
Divide the fourth term by the third: $\frac{27}{9} = 3$.

The correct option is A.

22.

n | 1 | 3 | 5 | 7
Tn | 5 | 1 | -3 | -7

When $n$ changes from 1 to 3 (change of $+2$), $T_n$ changes from 5 to 1 (change of $-4$).
When $n$ changes from 3 to 5 (change of $+2$), $T_n$ changes from 1 to $-3$ (change of $-4$).
This indicates a linear relationship of the form $T_n = mn + c$. The slope $m = \frac{\text{change in } T_n}{\text{change in } n} = \frac{-4}{2} = -2$.

Use one of the points from the table, for example, $(n=1, T_n=5)$.
$5 = -2(1) + c$
$5 = -2 + c$
$c = 5 + 2$
$c = 7$

$T_n = -2n + 7$.

The correct option is C.

23.

$3x^3 + 3x(x^2) + 3x^2 + 3x$.

The term $3x(x^2)$ can be simplified to $3x^{1+2} = 3x^3$.
So the expression becomes $3x^3 + 3x^3 + 3x^2 + 3x$.

From the simplified expression, the terms are $3x^3$, $3x^3$, $3x^2$, and $3x$.

A $3x^3$ and $3x(x^2)$: Since $3x(x^2) = 3x^3$, this pair consists of $3x^3$ and $3x^3$, which are like terms.

The correct option is A.

24.

$(-2x^2)^3$.

$(-2x^2)^3 = (-2)^3 \cdot (x^2)^3$

$(-2)^3 = -2 \times -2 \times -2 = -8$.
$(x^2)^3 = x^{2 \times 3} = x^6$.

The simplified term is $-8x^6$.

The coefficient is the numerical factor, which is $-8$.
The degree of the term is the exponent of the variable, which is 6.

The correct option is D.