What are the explicit equation and domain for a geometric sequence with a first term of 2 and a second term of −8? an = 2(−8)n − 1; all integers where n ≥ 1 an = 2(−8)n − 1; all integers where n ≥ 0 an = 2(−4)n − 1; all integers where n ≥ 0 an = 2(−4)n − 1; all integers where n ≥ 1

Answers

Answer 1

Answer: Hello,

The question is
"What are the explicit equation and domain for a geometric sequence with a first term of 2 and a second term of −8?"

It is a geometric sequence =>U(2)=U(1)*r==>-8=2*r ==>r=-4

U(1)=2=2*(-4)^0
U(2)=-8=2*(-4)=2*(-4)^1
U(3)=32=-8*(-4)=2*(-4)(-4)=2*(-4)^2
U(4)=-128=32*(-4)=2*(-4)^3
...
U(n)=2*(-4)^(n-1) where n>=1.

Answer C

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Use the REMAINDER THEOREM to explain whether or not (x-2) is a factor of F(x)=x^4-2x^3+3x^2-10x+3

Answers

$(P(x))/(R(x))|(D(x))/(Q(x))$

$\frac{x^4-2x^3+3x^2-10x+3}{}|\frac{x-2}{}$

$(x^4-2x^3+3x^2-10x+3)/(-x^4+2x^3)|(x-2)/(x^3)$

$(3x^2-10x+3)/(-3x^2+6x)|(x-2)/(x^3+3x)$

$(-4x+3)/(4x-8)|(x-2)/(x^3+3x-4)$

$\frac{-5}{}|(x-2)/(x^3+3x-4)$

$\boxed{\boxed{(x^4-2x^3+3x^2-10x+3)/(-5)|(x-2)/(x^3+3x-4)}}$

$R(x)=-5$