Let's find the initial terms of the sequence:
f(1) = 5
f(2) = 2*5 = 10
f(3) = 2*10 = 20
f(4) = 2*20 = 40
So, the ratio of the sequence is 2 = 40/20 = 20/10
And the general explicit formula is:
[tex]\begin{gathered} f_n=f_1\cdot r^{n-1} \\ \end{gathered}[/tex]
Substituting the values, we have the explicit formula for this sequence:
[tex]f_n=5\cdot2^{n-1}_{}[/tex]
f(1) means the first term of the sequence;
f(2) means the second term of the sequence;
f(n) is a general formula for the "n" term
So, f(n) = 2f(n-1) is a formula to find the term "n" using the term "n-1" (the antecessor).
Here, we have an example:
f(1) = 5
f(n) = 2f(n-1)
If n = 2
f(2) = 2*f(2-1)
f(2) = 2*f(1)
f(2) = 2*5
f(2) = 10
If n=3
f(3) = 2*f(3-1)
f(3) = 2*f(2)
f(3) = 2*10
f(3) = 20
