The formula f (x + 1) = Two-thirds (f (x)) defines a geometric sequence where f (1) = 18. Which explicit formula can be used to model the same sequence?

The explicit formula is Tn = 18[ (2/3) ^ (n-1) ]

Where n is the term we are looking for

Step-by-step explanation:

Here, we want to get an explicit formula to model the equation

Now, F (2) = 2/3 * f1 = 2/3 * 18 = 12

F (3) = 2/3 * f (2) = 2/3 * 12 = 8

F (4) = 2/3 * F (3) = 2/3 * 8 = 16/3

F (5) = 2/3 * 16/3 = 32/9

Thus, seeing how the equations are progressing, we can definitely see a pattern.

That is Tn = (2/3) ^ (n-1) (18)