Write the recurrence relation for the nth term which is defined by multiplying the prior term by 3 and subtracting 12.

Aₙ = 3*Aₙ₋₁ - 12

Step-by-step explanation:

Here our terms will be denoted as:

Aₙ

Where this is the n-th term of the sequence.

Now we have that the recurrence relation is defined by:

"by multiplying the prior term by 3 and subtracting 12."

Then we will have that:

Aₙ = 3*Aₙ₋₁ - 12

That is the equation to find all the terms in our sequence (remember that we need to know the initial term, A₀ in order to find all the other ones)

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.