Answer:
The sequence is given by,
f(n) = [tex]256 \times (1.25)^{(n - 1)}[/tex]
Step-by-step explanation:
Let the geometric sequence has 1st term = b and common ratio = r
so, the sequence is,
f(n) = [tex]b \times r^{(n - 1)}[/tex] ----------------------(1)
According to the question,
[tex]br = 320[/tex] ---------------------(2) and,
[tex]b \times r^{(5 - 1)}[/tex] = 625
⇒[tex]b \times r^{4}[/tex] = 625 --------------(3)
Now, dividing (3) by (2), we get,
[tex]r^{3} = \frac {625}{320}[/tex]
⇒[tex]r^{3} = \frac {125}{64}[/tex]
⇒[tex] r = \frac {5}{4}[/tex]
⇒ r = 1.25 -----------------------------------(4)
Now, from (2) and (4), we get,
b = [tex]\frac {320}{1.25}[/tex]
⇒ b = [tex]320 \times \frac {4}{5}[/tex]
⇒ b = 256-----------------(5)
So, from (4) and (5), the sequence is given by,
f(n) = [tex]256 \times (1.25)^{(n - 1)}[/tex]
