Answer:
The function defining the sequence is;
F(n) = 2.5•3^(n-1)
Step-by-step explanation:
Here, we want to find an expression that defines explicitly what is obtained in the sequence.
Checking the sequence, we can observe that the second term is 3 multiplied by the first term, the 3rd term is 3 multiplied by the second and so on
So what this means is that, the succeeding term is 3 times the preceding term;
Also, we can see that the first term is a factor of all the numbers and this mean that;
Second term = 3 * 2.5
Third term = 9 * 2.5 = 3^2 * 2.5
Fourth term 27 * 2.5 = 3^3 * 2.5
Thus, in function form;
F(1) = 2.5•3^(1-1)
F(2) = 2.5•3^(2-1)
F(3) = 2.5•3^(3-1)
Thus;
F(n) = 2.5•3^(n-1)
