Question 960751
First of all, that reply is not an answer lol. 
Ok, so to the solution. We know it is a geometric sequence so we need to find the ratio and the first term in order to find the sum.
Finding the first term is easy, if we take away 3 gallons of water and replace it with 3 gallons of alcohol then there are 9 gallons of water and 3 gallons of alcohol. So our first term is 3.
Finding the ratio is a bit more tricky. We need to find the second term. We know that 1/4 of the solution is alcohol so if we take out 3 gallons of the solution and 1/3 of 3 is 1 then we take out 1 gallon of alcohol then we add back in 3 gallon we know 2+3 is 5 so now there are 5 gallons of alcohol and 7 gallons of water. Now we know the ratio is 5/3.
Now we can plug it into the formula. {{{ S8=(3(5/3)^(8)-3)/(5/3-1) }}}. I'm not gonna show all the steps but you should get the answer. 
Note: I'm not entirely sure on the=is answer as I was having trouble on this problem as well :P