Question

Use the first five terms of sequence H to define the sequence recursively using

function notation. 2.5, 7.5, 22.5, 67.5, 202.5, ... *Remember: Find the growth
factor/rate of change first*
Helppp

Answer 1

The function defining the sequence is;

F(n) = 2.5•3^(n-1)

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)