I don't remember the entire question but here is the info I remember; for the sequence every term except for the first term is found by multiplying the previous term by 3 and subtracting by 1 and the difference between the 5th term and 3rd term is 28. Find the value of the first term of the sequence.

The 5th - 3rd = 28. By definition the 5th term is also 3(4th) - 1 and the 3rd term is 3(2nd) -1. Which means (3(4th) - 1)-(3(2nd)-1) = 28.
So
3(4th)-1-3(2nd)+1=28 or rather 3(4th)-3(2nd)=28.

Now factor out the 3, so you have 3(4th-2nd)=28.  
Because of the definition of this sequence, the next difference down must add another factor of three.
The difference between the 3rd and 1st term must be 3*3(3rd-1st) = 28, meaning (3rd - 1st) = 28/9.
Keep in mind, you don't need to find the answer, just do enough to eliminate most answer choices. There was only one answer with a 9 in the denominator, choose it.
I know, I know, I hear you in the second seat from the back, you are like "what"?

So let's see if this helps. Pick a easy number to use in the definition above.

Start with 1;
the first number = 1,
the second is 3(1)-1 = 2,
the third is 3(2)-1 = 5,
the fourth is 3(5)-1=14,
the fifth is 3(14)-1=41.
The difference between the fifth term and the third is 41-5=36.
The difference between the fourth term and second term is 14-2=12.
The difference between the third term and the first term is 5-1=4.
Each one of these differences can be viewed as increasing factors of 3.
4 = 4*3^0
12 = 4*3^1
36 = 4*3^2
So without computing the sixth term, the difference between the sixth and fourth term will be 4*3^3 =108. That means I can find the sixth term by adding 108 to the fourth term.

Once you recognize the pattern you can go up and down as needed to answer the question. If you want to actually find the value of the first term we could do that as well but it is not necessary to answer the question since it is multiple choice.

Student Getting Help From a Sibling

An eager math student wanted to move ahead in class and started working on topics the instructor had not covered yet. The student came across 5! and did not know what to do, so the student asked an older brother what 5! meant. The older brother's response is in the following video clip.