The term to term rule is divide by 2 the third term of the sequence is 3 work out the first term

12

Step-by-step explanation:

if the term to term rule is to divide by two and the third term in the sequence is 3, you work backwards by multiplying by 2

So 3x2=6

6x2= 12

Thus the first number is 12.

working forward again, you can check your answer. Divide 12 by 2, then divide 6 by 2 and you get 3, the third term if the sequence

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0