If
is the first number in the progression, and
is the common ratio between consecutive terms, then the first four terms in the progression are

We want to have

In the second equation, we have

and in the first, we have

Substituting this into the second equation, we find

So now we have

Then the four numbers are

Seven hundred is the value of the seven in 43,782
Roger needs to score 1163 more points to win the game.
Ln(xy) - 2x =0
slope of the tangent line = derivative of the function
[ln(xy)]' = [2x]'
[1/(xy)] [y + xy'] = 2
y + xy' = 2(xy)
xy' = 2xy - y =y(2x-1)
y' = y(2x-1)/x
Now use x = -1 to find y and after to find y'
ln(xy) = 2x
x=-1
ln(-y) =-2
-y = e^-2
y = - e^-2
y' = [-e^-2][2(-1)-1]/(-1) = [e^-2](-2-1)= [e^-2](-3) = - 3e^-2
Answer: option 6. from the list