There can be a lot of way to figure these types of problems out.One things that is going on, one can tell, is that we are multiplying each number by 3 to get the next number (3*4=12, 12*3=36). But, that doesn’t us a formula.
Given that this is multiplication, we see that this is a geometric sequence. So, the formula would be of the form y= a*b^x. We are looking for numbers for a and b. The way we do that is first consider how the numbers are arranged, as in:
n number y
1 4
2 12
3 36
Where “n numbers “ represents “ the first number”, the second number”, etc. And y is the actual number. So, then, we can have coordinate points (1,4) (2,12) and (3,36)
Plugging any 2 of these into the general formula would give us something like:
4=a*b^1 and 12= a*b^2
The first one simplifies to:
4=a*b Or a=4/b
Substituting that into the second equation, we get:
12= (4/b)*b^2= 4*(b^2)/b=4*b
12=4b
So, b=3
Subbing this into the first equation we made, 4=a*b:
4=a*3
a=4/3
So, formula for this sequence is:
Y=(4/3)*3^x Or, we can use n for the number of the term
Y=(4/3)*3^n
So, then, if we want the first number, n=1
Y=4/3*3^1=4/3*3=4
For the second number, n=2
Y=(4/3)*3^2=(4/3)*9=12
